Pub Date : 2022-03-31DOI: 10.18500/0869-6632-2022-30-2-132-151
A. Kornuta, V. Lukianenko
Purpose of this work is to study the initial-boundary value problem for a parabolic functional-differential equation in an annular region, which describes the dynamics of phase modulation of a light wave passing through a thin layer of a nonlinear Kerr-type medium in an optical system with a feedback loop, with a rotation transformation (corresponds the involution operator) and the Neumann conditions on the boundary in the class of periodic functions. A more detailed study is made of spatially inhomogeneous stationary solutions bifurcating from a spatially homogeneous stationary solution as a result of a bifurcation of the “fork” type and time-periodic solutions of the “traveling wave” type. Methods. To represent the original equation in the form of nonlinear integral equations, the Green’s function is used. The method of central manifolds is used to prove the theorem on the existence of solutions of the indicated equation in a neighborhood of the bifurcation parameter and to study their asymptotic form. Numerical modeling of spatially inhomogeneous solutions and traveling waves was carried out using the Galerkin method. Results. Integral representations of the considered problem are obtained depending on the form of the linearized operator. Using the method of central manifolds, a theorem on the existence and asymptotic form of solutions of the initial-boundary value problem for a functional-differential equation of parabolic type with an involution operator on an annulus is proved. As a result of numerical modeling based on Galerkin approximations, in the problem under consideration, approximate spatially inhomogeneous stationary solutions and time-periodic solutions of the traveling wave type are constructed. Conclusion. The proposed scheme is applicable not only to involutive rotation operators and Neumann conditions on the boundary of the ring, but also to other boundary conditions and circular domains. The representation of the initial-boundary value problem in the form of nonlinear integral equations of the second kind allows one to more simply find the coefficients of asymptotic expansions, prove existence and uniqueness theorems, and also use a different number of expansion coefficients of the nonlinear component in the right-hand side of the original equation in the neighborhood of the selected solution (for example, stationary). Visualization of the numerical solution confirms the theoretical calculations and shows the possibility of forming complex phase structures.
{"title":"Dynamics of solutions of nonlinear functional differential equation of parabolic type","authors":"A. Kornuta, V. Lukianenko","doi":"10.18500/0869-6632-2022-30-2-132-151","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-2-132-151","url":null,"abstract":"Purpose of this work is to study the initial-boundary value problem for a parabolic functional-differential equation in an annular region, which describes the dynamics of phase modulation of a light wave passing through a thin layer of a nonlinear Kerr-type medium in an optical system with a feedback loop, with a rotation transformation (corresponds the involution operator) and the Neumann conditions on the boundary in the class of periodic functions. A more detailed study is made of spatially inhomogeneous stationary solutions bifurcating from a spatially homogeneous stationary solution as a result of a bifurcation of the “fork” type and time-periodic solutions of the “traveling wave” type. Methods. To represent the original equation in the form of nonlinear integral equations, the Green’s function is used. The method of central manifolds is used to prove the theorem on the existence of solutions of the indicated equation in a neighborhood of the bifurcation parameter and to study their asymptotic form. Numerical modeling of spatially inhomogeneous solutions and traveling waves was carried out using the Galerkin method. Results. Integral representations of the considered problem are obtained depending on the form of the linearized operator. Using the method of central manifolds, a theorem on the existence and asymptotic form of solutions of the initial-boundary value problem for a functional-differential equation of parabolic type with an involution operator on an annulus is proved. As a result of numerical modeling based on Galerkin approximations, in the problem under consideration, approximate spatially inhomogeneous stationary solutions and time-periodic solutions of the traveling wave type are constructed. Conclusion. The proposed scheme is applicable not only to involutive rotation operators and Neumann conditions on the boundary of the ring, but also to other boundary conditions and circular domains. The representation of the initial-boundary value problem in the form of nonlinear integral equations of the second kind allows one to more simply find the coefficients of asymptotic expansions, prove existence and uniqueness theorems, and also use a different number of expansion coefficients of the nonlinear component in the right-hand side of the original equation in the neighborhood of the selected solution (for example, stationary). Visualization of the numerical solution confirms the theoretical calculations and shows the possibility of forming complex phase structures.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"14 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75467168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-31DOI: 10.18500/0869-6632-2022-30-2-176-188
Marina Nikulina, V. Antonets
The objective of this study is to show the possibility of using the smoothing cardiointervalograms (CIG) method which is solely time domain analysis of CIG to separate and display the influence of various mechanisms of human physiological regulation systems on his heart rate. Methods.This paper shows the possibility of using the method of smoothing the cardiointervalogram by means of a moving average for its subsequent decomposition into slow and fast components. Decomposition results are visualized by line graphs and pseudo-phase portraits. Visualization settings allow us to isolate unique transients and calculate its timing. The method is applied to data obtained under different subject functional states and differing in the level of adaptation risks, the presence or absence of stress. For analysis were selected stress episodes detected using the information and telecommunication technology of event-related cardiac telemetry (ITT ERCT) presented by the Internet resource “StressMonitor”. Results.For the numerical series of RR-intervals, a clear division into fast and slow components is obtained. An algorithm for identifying the frequency content of heart rate variability has been formulated and tested. A visualization method is proposed that is convenient for comparing data obtained for different patients. A pseudo-phase portrait pattern corresponding to the moment of stress onset is found. The proposed method reduced the discreteness of identifying the stress onset moment from 10 seconds to single heart beats. Conclusion. The correspondence of the results to the verified ITT ERCT method and the Baevsky–Chernikova concept of adaptive risk has been demonstrated. This confirms the possibility of using the time cardiointervalograms smoothing method for the analysis of heart rate variability.
{"title":"Experience in assessing heart rate variability by smoothed cardiointervalograms","authors":"Marina Nikulina, V. Antonets","doi":"10.18500/0869-6632-2022-30-2-176-188","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-2-176-188","url":null,"abstract":"The objective of this study is to show the possibility of using the smoothing cardiointervalograms (CIG) method which is solely time domain analysis of CIG to separate and display the influence of various mechanisms of human physiological regulation systems on his heart rate. Methods.This paper shows the possibility of using the method of smoothing the cardiointervalogram by means of a moving average for its subsequent decomposition into slow and fast components. Decomposition results are visualized by line graphs and pseudo-phase portraits. Visualization settings allow us to isolate unique transients and calculate its timing. The method is applied to data obtained under different subject functional states and differing in the level of adaptation risks, the presence or absence of stress. For analysis were selected stress episodes detected using the information and telecommunication technology of event-related cardiac telemetry (ITT ERCT) presented by the Internet resource “StressMonitor”. Results.For the numerical series of RR-intervals, a clear division into fast and slow components is obtained. An algorithm for identifying the frequency content of heart rate variability has been formulated and tested. A visualization method is proposed that is convenient for comparing data obtained for different patients. A pseudo-phase portrait pattern corresponding to the moment of stress onset is found. The proposed method reduced the discreteness of identifying the stress onset moment from 10 seconds to single heart beats. Conclusion. The correspondence of the results to the verified ITT ERCT method and the Baevsky–Chernikova concept of adaptive risk has been demonstrated. This confirms the possibility of using the time cardiointervalograms smoothing method for the analysis of heart rate variability.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91333336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-31DOI: 10.18500/0869-6632-2022-30-2-152-175
D. Glyzin, S. Glyzin, A. Kolesov
The purpose of this work is to study the dynamic properties of solutions to special systems of ordinary differential equations, called fully connected networks of nonlinear oscillators. Methods. A new approach to obtain periodic regimes of the chimeric type in these systems is proposed, the essence of which is as follows. First, in the case of a symmetric network, a simpler problem is solved of the existence and stability of quasi-chimeric solutions — periodic regimes of two-cluster synchronization. For each of these modes, the set of oscillators falls into two disjoint classes. Within these classes, full synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously. Results. On the basis of the proposed methods, it is separately established that in the transition from a symmetric system to a general network, the periodic regimes of two-cluster synchronization can be transformed into chimeras. Conclusion. The main statements of the work concerning the emergence of chimeras were obtained analytically on the basis of an asymptotic study of a model example. For this example, the notion of a canonical chimera is introduced and the statement about the existence and stability of solutions of chimeric type in the case of asymmetry of the network is proved. All the results presented are extended to a continuous analogue of the corresponding system. The obtained results are illustrated numerically.
{"title":"Hunt for chimeras in fully coupled networks of nonlinear oscillators","authors":"D. Glyzin, S. Glyzin, A. Kolesov","doi":"10.18500/0869-6632-2022-30-2-152-175","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-2-152-175","url":null,"abstract":"The purpose of this work is to study the dynamic properties of solutions to special systems of ordinary differential equations, called fully connected networks of nonlinear oscillators. Methods. A new approach to obtain periodic regimes of the chimeric type in these systems is proposed, the essence of which is as follows. First, in the case of a symmetric network, a simpler problem is solved of the existence and stability of quasi-chimeric solutions — periodic regimes of two-cluster synchronization. For each of these modes, the set of oscillators falls into two disjoint classes. Within these classes, full synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously. Results. On the basis of the proposed methods, it is separately established that in the transition from a symmetric system to a general network, the periodic regimes of two-cluster synchronization can be transformed into chimeras. Conclusion. The main statements of the work concerning the emergence of chimeras were obtained analytically on the basis of an asymptotic study of a model example. For this example, the notion of a canonical chimera is introduced and the statement about the existence and stability of solutions of chimeric type in the case of asymmetry of the network is proved. All the results presented are extended to a continuous analogue of the corresponding system. The obtained results are illustrated numerically.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"12 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82334677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-31DOI: 10.18500/0869-6632-2022-30-2-189-207
E. Grigorieva, S. Kashchenko
Purpose. The local dynamics of the laser chain model with optoelectronic delayed unidirectional coupling is investigated. A system of equations is considered that describes the dynamics of a closed chain of a large number of lasers with optoelectronic delayed coupling between elements. An equivalent distributed integro-differential model with a small parameter inversely proportional to the number of lasers in the chain is proposed. For a distributed model with periodic edge conditions, the critical value of the coupling coefficient is obtained, at which the stationary state in the chain becomes unstable. It is shown that in a certain neighborhood of the bifurcation point, the number of roots of the characteristic equation with a real part close to zero increases indefinitely when the small parameter decreases. In this case, a two-dimensional complex Ginzburg–Landau equation with convection is constructed as a normal form. Its nonlocal dynamics determines the behavior of the solutions of the original boundary value problem. Research methods. Methods for studying local dynamics based on the construction of normal forms on central manifolds are used as applied to critical cases of (asymptotically) infinite dimension. An algorithm for reducing the original boundary value problem to the equation for slowly varying amplitudes is proposed. Results. The simplest homogeneous periodic solutions of Ginzburg–Landau equation and corresponding to them inhomogeneous solutions in the form of traveling waves in a distributed model are obtained. Such solutions can be interpreted as phase locking regimes in the chain of coupled lasers. The frequencies and amplitudes of oscillations of the radiation intensity of each laser and the phase difference between adjacent oscillators are determined.
{"title":"Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling","authors":"E. Grigorieva, S. Kashchenko","doi":"10.18500/0869-6632-2022-30-2-189-207","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-2-189-207","url":null,"abstract":"Purpose. The local dynamics of the laser chain model with optoelectronic delayed unidirectional coupling is investigated. A system of equations is considered that describes the dynamics of a closed chain of a large number of lasers with optoelectronic delayed coupling between elements. An equivalent distributed integro-differential model with a small parameter inversely proportional to the number of lasers in the chain is proposed. For a distributed model with periodic edge conditions, the critical value of the coupling coefficient is obtained, at which the stationary state in the chain becomes unstable. It is shown that in a certain neighborhood of the bifurcation point, the number of roots of the characteristic equation with a real part close to zero increases indefinitely when the small parameter decreases. In this case, a two-dimensional complex Ginzburg–Landau equation with convection is constructed as a normal form. Its nonlocal dynamics determines the behavior of the solutions of the original boundary value problem. Research methods. Methods for studying local dynamics based on the construction of normal forms on central manifolds are used as applied to critical cases of (asymptotically) infinite dimension. An algorithm for reducing the original boundary value problem to the equation for slowly varying amplitudes is proposed. Results. The simplest homogeneous periodic solutions of Ginzburg–Landau equation and corresponding to them inhomogeneous solutions in the form of traveling waves in a distributed model are obtained. Such solutions can be interpreted as phase locking regimes in the chain of coupled lasers. The frequencies and amplitudes of oscillations of the radiation intensity of each laser and the phase difference between adjacent oscillators are determined.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"20 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89110437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.18500/0869-6632-2022-30-1-76-95
P. Chholak, Fatemeh Tabari, A. Pisarchik
The ability to name trivial everyday objects is a key cognitive function that is tested after head injuries or brain surgeries. Although quite a lot of long-standing knowledge on this topic has accumulated over the past few decades and many theoretical models have been created, the underlying neural substrate and brain functioning are still not fully aligned. As far as we know, there have been no studies on this topic using magnetoencephalography (MEG), which allows recording electrophysiological activity with a high temporal resolution. Therefore, to study the underlying spatio-temporal brain activations during the sensory and semantic processing of object naming, we conducted MEG experiments with 15 subjects grouped into three equal-sized groups with different types of language training and skills. Using boundary element methods for modelling cortical surfaces and dynamic statistical parametric mapping to solve the inverse problem, we reconstructed the cortical source activity from the recorded MEG data. The reconstructed cortical maps showed a homogeneous brain response in all three groups at the sensory processing stage, while the responses between the three groups at the semantic processing stage were different. In addition, average time courses were constructed for key brain regions such as the lateral occipital cortex (LO), fusiform gyrus (FG), Broca’s area (BA), and Wernicke’s area (WA). The obtained results assume unimodal forms for LO and WA time series, and bimodal forms for FG and BA. The only LO curve peak and the first FG peak resided in the time interval for the sensory processing stage, whereas, the only WA peak, the second FG peak and the second BA peak resided in the semantic processing stage. The first BA peak was located at the boundary separating the two stages. In addition to segregating regions involved in sensory and semantic processing, this study confirmed the involvement of FG in object naming (for the first time using MEG) that is at risk of resection during mesial temporal lobe epilepsy interventions. However, the results from this work are preliminary due to the limited sample size, and future research with a larger cohort of subjects are needed to verify/strengthen the findings of this study.
{"title":"Revealing the neural network underlying covert picture-naming paradigm using magnetoencephalography","authors":"P. Chholak, Fatemeh Tabari, A. Pisarchik","doi":"10.18500/0869-6632-2022-30-1-76-95","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-1-76-95","url":null,"abstract":"The ability to name trivial everyday objects is a key cognitive function that is tested after head injuries or brain surgeries. Although quite a lot of long-standing knowledge on this topic has accumulated over the past few decades and many theoretical models have been created, the underlying neural substrate and brain functioning are still not fully aligned. As far as we know, there have been no studies on this topic using magnetoencephalography (MEG), which allows recording electrophysiological activity with a high temporal resolution. Therefore, to study the underlying spatio-temporal brain activations during the sensory and semantic processing of object naming, we conducted MEG experiments with 15 subjects grouped into three equal-sized groups with different types of language training and skills. Using boundary element methods for modelling cortical surfaces and dynamic statistical parametric mapping to solve the inverse problem, we reconstructed the cortical source activity from the recorded MEG data. The reconstructed cortical maps showed a homogeneous brain response in all three groups at the sensory processing stage, while the responses between the three groups at the semantic processing stage were different. In addition, average time courses were constructed for key brain regions such as the lateral occipital cortex (LO), fusiform gyrus (FG), Broca’s area (BA), and Wernicke’s area (WA). The obtained results assume unimodal forms for LO and WA time series, and bimodal forms for FG and BA. The only LO curve peak and the first FG peak resided in the time interval for the sensory processing stage, whereas, the only WA peak, the second FG peak and the second BA peak resided in the semantic processing stage. The first BA peak was located at the boundary separating the two stages. In addition to segregating regions involved in sensory and semantic processing, this study confirmed the involvement of FG in object naming (for the first time using MEG) that is at risk of resection during mesial temporal lobe epilepsy interventions. However, the results from this work are preliminary due to the limited sample size, and future research with a larger cohort of subjects are needed to verify/strengthen the findings of this study.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"5 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84177862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.18500/0869-6632-2022-30-1-7-29
S. Kuznetsov, L. Turukina
The purpose of this work is to numerically study of the generalized Rabinovich–Fabrikant model. This model is obtained using the Lagrange formalism and describing the three-mode interaction in the presence of a general cubic nonlinearity. The model demonstrates very rich dynamics due to the presence of third-order nonlinearity in the equations. Methods. The study is based on the numerical solution of the obtained analytically differential equations, and their numerical bifurcation analysis using the MаtCont program. Results. For the generalized model we present a charts of dynamic regimes in the control parameter plane, Lyapunov exponents depending on parameters, portraits of attractors and their basins. On the plane of control parameters, bifurcation lines and points are numerically found. They are plotted for equilibrium point and period one limit cycle. It is shown that the dynamics of the generalized model depends on the signature of the characteristic expressions presented in the equations. A comparison with the dynamics of the Rabinovich– Fabrikant model is carried out. We indicated a region in the parameter plane in which there is a complete or partial coincidence of dynamics. Conclusion. The generalized model is new and describes the interaction of three modes, in the case when the cubic nonlinearity that determines their interaction is given in a general form. In addition, since the considered model is a certain natural extension of the well-known Rabinovich–Fabrikant model, then it is universal. And it can simulate systems of various physical nature (including radio engineering), in which there is a three-mode interaction and there is a general cubic nonlinearity.
{"title":"Generalized Rabinovich–Fabrikant system: equations and its dynamics","authors":"S. Kuznetsov, L. Turukina","doi":"10.18500/0869-6632-2022-30-1-7-29","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-1-7-29","url":null,"abstract":"The purpose of this work is to numerically study of the generalized Rabinovich–Fabrikant model. This model is obtained using the Lagrange formalism and describing the three-mode interaction in the presence of a general cubic nonlinearity. The model demonstrates very rich dynamics due to the presence of third-order nonlinearity in the equations. Methods. The study is based on the numerical solution of the obtained analytically differential equations, and their numerical bifurcation analysis using the MаtCont program. Results. For the generalized model we present a charts of dynamic regimes in the control parameter plane, Lyapunov exponents depending on parameters, portraits of attractors and their basins. On the plane of control parameters, bifurcation lines and points are numerically found. They are plotted for equilibrium point and period one limit cycle. It is shown that the dynamics of the generalized model depends on the signature of the characteristic expressions presented in the equations. A comparison with the dynamics of the Rabinovich– Fabrikant model is carried out. We indicated a region in the parameter plane in which there is a complete or partial coincidence of dynamics. Conclusion. The generalized model is new and describes the interaction of three modes, in the case when the cubic nonlinearity that determines their interaction is given in a general form. In addition, since the considered model is a certain natural extension of the well-known Rabinovich–Fabrikant model, then it is universal. And it can simulate systems of various physical nature (including radio engineering), in which there is a three-mode interaction and there is a general cubic nonlinearity.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"4 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84969977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.18500/0869-6632-2022-30-1-37-56
V. Zakovorotny, Valeriya Gvindjiliya
Nowadays, the dynamic cutting system is represented in the form of two subsystems — tool and workpiece, interacting through a nonlinear relationship formed by the cutting process. Such a representation determines the importance of studying the dynamics of the cutting process as the main factor influencing the efficiency of machines, the trajectories of the executive elements of which are set by CNC and are provided with high accuracy. However, in order to improve the efficiency of cutting, it is necessary to align the trajectories of the executive elements are defined by CNC with the changing dynamics of cutting, which introduces deviations in the program-defined trajectories. Purpose of this article is to consider the dependence of the dynamics of the cutting process on the spatial orientation of the cutting tool elasticity and the regenerative effect, and to find out the effect of the proposed dependence on the efficiency of the cutting process. All the issues discussed in the article are analyzed using the example of external shaft turning. Methods. The study is based on the methods of mathematical modeling and experimental dynamics. In contrast to the known studies, the dependence of the turnover lag time on the oscillatory displacements in the direction of the cutting speed, as well as the influence of the positive feedback formed in this case, is taken into account. In addition, changes in the sign of the internal feedback from the direction of deformations, as well as the influence of the regenerative effect on the generated attracting sets of deformations are taken into account. Results. Dependence of the system evolution on the elements of the stiffness matrix at different spindle speeds is disclosed. The properties of the system evolution depending on the ratio of the spindle rotation frequency and the eigenfrequencies of the tool subsystem, as well as the spatial distribution of the stiffness are studied. Conclusion. The frequency and time characteristics of the system are discussed. Conclusion is made about the possibility of efficiency increasing of the cutting process based on the coordination of the CNC program with the dynamic properties of the system.
{"title":"Correlation of attracting sets of tool deformations with spatial orientation of tool elasticity and regeneration of cutting forces in turning","authors":"V. Zakovorotny, Valeriya Gvindjiliya","doi":"10.18500/0869-6632-2022-30-1-37-56","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-1-37-56","url":null,"abstract":"Nowadays, the dynamic cutting system is represented in the form of two subsystems — tool and workpiece, interacting through a nonlinear relationship formed by the cutting process. Such a representation determines the importance of studying the dynamics of the cutting process as the main factor influencing the efficiency of machines, the trajectories of the executive elements of which are set by CNC and are provided with high accuracy. However, in order to improve the efficiency of cutting, it is necessary to align the trajectories of the executive elements are defined by CNC with the changing dynamics of cutting, which introduces deviations in the program-defined trajectories. Purpose of this article is to consider the dependence of the dynamics of the cutting process on the spatial orientation of the cutting tool elasticity and the regenerative effect, and to find out the effect of the proposed dependence on the efficiency of the cutting process. All the issues discussed in the article are analyzed using the example of external shaft turning. Methods. The study is based on the methods of mathematical modeling and experimental dynamics. In contrast to the known studies, the dependence of the turnover lag time on the oscillatory displacements in the direction of the cutting speed, as well as the influence of the positive feedback formed in this case, is taken into account. In addition, changes in the sign of the internal feedback from the direction of deformations, as well as the influence of the regenerative effect on the generated attracting sets of deformations are taken into account. Results. Dependence of the system evolution on the elements of the stiffness matrix at different spindle speeds is disclosed. The properties of the system evolution depending on the ratio of the spindle rotation frequency and the eigenfrequencies of the tool subsystem, as well as the spatial distribution of the stiffness are studied. Conclusion. The frequency and time characteristics of the system are discussed. Conclusion is made about the possibility of efficiency increasing of the cutting process based on the coordination of the CNC program with the dynamic properties of the system.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"2013 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73972166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.18500/0869-6632-2022-30-1-30-36
G. Sizykh
Purpose of the study is to obtain formulas for such a speed of imaginary particles that the circulation of the speed of a (real) fluid along any circuit consisting of these imaginary particles changes (in the process of motion of imaginary particles) according to a given time law. (Until now, only those speeds of imaginary particles were known, at which the mentioned circulation during the motion remained unchanged). Method. Without implementation of asymptotic, numerical and other approximate methods, a rigorous analysis of the dynamic equation of motion (flow) of any continuous fluid medium, from an ideal liquid to a viscous gas, is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. The concept of motion of imaginary particles is used, based on the K. Zoravsky criterion (which is also called A. A. Fridman’s theorem). Results. Formulas for the speed of imaginary particles are proposed. These formulas include the parameters of the (real) flow, their spatial derivatives and the function of time, which determines the law of the change in time of the (real fluid) velocity circulation along the contours moving together with the imaginary particles. In addition, it turned out that for a given function of time (and, as a consequence, for a given law of change in circulation with respect to time), the speed of imaginary particles is determined ambiguously. As a result, a method is proposed to change the speed and direction of motion of imaginary particles in a certain range (while maintaining the selected law of changes in circulation in time). For a viscous incompressible fluid, formulas are proposed that do not include pressure and its derivatives. Conclusion. A new Lagrangian point of view on the vorticity evolution in two-dimensional flows of fluids of all types is proposed. Formulas are obtained for the velocity of such movement of contours, at which the real fluid velocity circulation along any contour changes according to a given time law. This theoretical result can be used in computational fluid dynamics to limit the number of domains when using a gridless method for calculating flows of a viscous incompressible fluid (the method of viscous vortex domains).
研究的目的是得到这样一个虚粒子速度的公式，即(真实)流体的速度沿着由这些虚粒子组成的任何回路(在虚粒子的运动过程中)按照给定的时间规律发生变化。(到目前为止，只有那些假想粒子的速度是已知的，在这些速度下，上述运动中的循环保持不变)。方法。在不采用渐近、数值和其他近似方法的情况下，对任何连续流体介质(从理想液体到粘性气体)的运动(流动)动力学方程进行了严格的分析。考虑了平面平行和非旋流轴对称流动。基于K. Zoravsky准则(也称为A. A. Fridman定理)，使用了虚粒子的运动概念。结果。提出了虚粒子速度的计算公式。这些公式包括(实)流的参数、它们的空间导数和时间函数，它们决定了(实)流体沿着与虚粒子一起运动的等高线的速度循环的时间变化规律。此外，事实证明，对于给定的时间函数(因此，对于给定的关于时间的循环变化规律)，虚粒子的速度是模糊确定的。因此，提出了一种在一定范围内改变虚粒子运动速度和方向的方法(同时保持所选择的循环随时间变化规律)。对于粘性不可压缩流体，提出了不包括压力及其导数的公式。结论。提出了一种新的拉格朗日观点来研究二维流体中涡度的演化。得到了等高线运动速度的公式，在等高线运动速度下，流体沿等高线的实际流速按给定的时间规律变化。这一理论结果可用于计算流体动力学中，在使用无网格方法计算粘性不可压缩流体的流动(粘性涡域法)时限制域的数量。
{"title":"New Lagrangian view of vorticity evolution in two-dimensional flows of liquid and gas","authors":"G. Sizykh","doi":"10.18500/0869-6632-2022-30-1-30-36","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-1-30-36","url":null,"abstract":"Purpose of the study is to obtain formulas for such a speed of imaginary particles that the circulation of the speed of a (real) fluid along any circuit consisting of these imaginary particles changes (in the process of motion of imaginary particles) according to a given time law. (Until now, only those speeds of imaginary particles were known, at which the mentioned circulation during the motion remained unchanged). Method. Without implementation of asymptotic, numerical and other approximate methods, a rigorous analysis of the dynamic equation of motion (flow) of any continuous fluid medium, from an ideal liquid to a viscous gas, is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. The concept of motion of imaginary particles is used, based on the K. Zoravsky criterion (which is also called A. A. Fridman’s theorem). Results. Formulas for the speed of imaginary particles are proposed. These formulas include the parameters of the (real) flow, their spatial derivatives and the function of time, which determines the law of the change in time of the (real fluid) velocity circulation along the contours moving together with the imaginary particles. In addition, it turned out that for a given function of time (and, as a consequence, for a given law of change in circulation with respect to time), the speed of imaginary particles is determined ambiguously. As a result, a method is proposed to change the speed and direction of motion of imaginary particles in a certain range (while maintaining the selected law of changes in circulation in time). For a viscous incompressible fluid, formulas are proposed that do not include pressure and its derivatives. Conclusion. A new Lagrangian point of view on the vorticity evolution in two-dimensional flows of fluids of all types is proposed. Formulas are obtained for the velocity of such movement of contours, at which the real fluid velocity circulation along any contour changes according to a given time law. This theoretical result can be used in computational fluid dynamics to limit the number of domains when using a gridless method for calculating flows of a viscous incompressible fluid (the method of viscous vortex domains).","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"27 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86693273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-31DOI: 10.18500/0869-6632-2022-30-1-109-124
A. Shabunin
Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters. Correlation between the spatial spectra and the amplitude-frequency response of the coupling filter and the mutual coherence of oscillations when the coupling parameters change were considered. Results. The system of couplings between chaotic maps behaves like a wave filter with selective properties, allowing spatial modes with certain wavelengths to exist and suppressing others. The selection of spatial modes is based on the wave characteristic of the coupling filter, the type of which is determined by the radius and the magnitude of couplings. At strong coupling the wave characteristics for ensembles with local and non-local couplings are qualitatively different, therefore they demonstrate essencially different behavior. Discussion. Using spectral methods for dynamics analysis systems with complex network topologies seems to be a promising approach, especially for research of synchronization and multistability in ensembles of chaotic oscillators and maps. The found regularities generalize the results known for ensembles of maps with local couplings. They also can be applied to ensembles of self-sustained oscillators.
{"title":"Selection of spatial modes in an ensemble of non-locally coupled chaotic maps","authors":"A. Shabunin","doi":"10.18500/0869-6632-2022-30-1-109-124","DOIUrl":"https://doi.org/10.18500/0869-6632-2022-30-1-109-124","url":null,"abstract":"Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters. Correlation between the spatial spectra and the amplitude-frequency response of the coupling filter and the mutual coherence of oscillations when the coupling parameters change were considered. Results. The system of couplings between chaotic maps behaves like a wave filter with selective properties, allowing spatial modes with certain wavelengths to exist and suppressing others. The selection of spatial modes is based on the wave characteristic of the coupling filter, the type of which is determined by the radius and the magnitude of couplings. At strong coupling the wave characteristics for ensembles with local and non-local couplings are qualitatively different, therefore they demonstrate essencially different behavior. Discussion. Using spectral methods for dynamics analysis systems with complex network topologies seems to be a promising approach, especially for research of synchronization and multistability in ensembles of chaotic oscillators and maps. The found regularities generalize the results known for ensembles of maps with local couplings. They also can be applied to ensembles of self-sustained oscillators.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":"37 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88463439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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