Pub Date : 2023-01-01DOI: 10.18500/0869-6632-003021
I. Safarov, M. Teshaev
The study of the problem of damping vibrations of a solid body mounted on viscoelastic supports is an urgent task. The paper considers the problem of reducing the level of vibrations on the paws of electric machines using dynamic vibration dampers. For this purpose, the paw of electric machines is represented in the form of a subamortized solid body with six degrees of freedom mounted on viscoelastic supports. The aim of the work is to develop calculation methods and algorithms for studying the oscillations of the resonant amplitudes of a solid body mounted on viscoelastic supports. Dynamic oscillation (vibration) damping method consists in attaching a system to the protected object, the reactions of which reduce the scope of vibration of the object at the points of attachment of this system. Applying the D’Alembert principle, the equations of small vibrations of a solid with dampers are derived. For practical calculations, a simplified system of equations was obtained that takes into account only three degrees of freedom. Numerical calculations were carried out on a computer to determine the amplitude-frequency characteristics of the main body. Numerical experiments were carried out using the Matlab mathematical package. Considering that a solid body is characterized by vibration, as a rule, in a continuous and wide frequency range, therefore, dynamic vibration dampers are used to protect a solid body mounted on viscoelastic supports. It was found that when the damper is set at a frequency of 50 Hz, the vibration level at the left end of the frequency interval of rotary motion of the rotor-converter, decreases to 37.5 dB, and at the right end — to 42.5 dB. At a frequency of 50 Hz, the paws do not oscillate. When setting the dampers to a frequency of 51.5 Hz, the maximum vibration level does not exceed 40 dB. The optimal setting of the dampers is within the frequency of 50.60...50.70 Hz, and a two-mass extinguisher is 10–15% more efficient than a single-mass one. Thus, the paper sets the tasks of dynamic damping of vibrations of a solid body mounted on viscoelastic supports, develops solution methods and an algorithm for determining the dynamic state of a solid body with passive vibration of the object in question.
{"title":"Dynamic damping of vibrations of a solid body mounted on viscoelastic supports","authors":"I. Safarov, M. Teshaev","doi":"10.18500/0869-6632-003021","DOIUrl":"https://doi.org/10.18500/0869-6632-003021","url":null,"abstract":"The study of the problem of damping vibrations of a solid body mounted on viscoelastic supports is an urgent task. The paper considers the problem of reducing the level of vibrations on the paws of electric machines using dynamic vibration dampers. For this purpose, the paw of electric machines is represented in the form of a subamortized solid body with six degrees of freedom mounted on viscoelastic supports. The aim of the work is to develop calculation methods and algorithms for studying the oscillations of the resonant amplitudes of a solid body mounted on viscoelastic supports. Dynamic oscillation (vibration) damping method consists in attaching a system to the protected object, the reactions of which reduce the scope of vibration of the object at the points of attachment of this system. Applying the D’Alembert principle, the equations of small vibrations of a solid with dampers are derived. For practical calculations, a simplified system of equations was obtained that takes into account only three degrees of freedom. Numerical calculations were carried out on a computer to determine the amplitude-frequency characteristics of the main body. Numerical experiments were carried out using the Matlab mathematical package. Considering that a solid body is characterized by vibration, as a rule, in a continuous and wide frequency range, therefore, dynamic vibration dampers are used to protect a solid body mounted on viscoelastic supports. It was found that when the damper is set at a frequency of 50 Hz, the vibration level at the left end of the frequency interval of rotary motion of the rotor-converter, decreases to 37.5 dB, and at the right end — to 42.5 dB. At a frequency of 50 Hz, the paws do not oscillate. When setting the dampers to a frequency of 51.5 Hz, the maximum vibration level does not exceed 40 dB. The optimal setting of the dampers is within the frequency of 50.60...50.70 Hz, and a two-mass extinguisher is 10–15% more efficient than a single-mass one. Thus, the paper sets the tasks of dynamic damping of vibrations of a solid body mounted on viscoelastic supports, develops solution methods and an algorithm for determining the dynamic state of a solid body with passive vibration of the object in question.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84877027","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 : 2023-01-01DOI: 10.18500/0869-6632-003038
Buu Hoang Nguyen, V. Tsybulin
Purpose of this work is to analyze oscillatory regimes in a system of nonlinear differential equations describing the competition of three non-antagonistic species in a spatially homogeneous domain. Methods. Using the theory of cosymmetry, we establish a connection between the destruction of a two-parameter family of equilibria and the emergence of a continuous family of periodic regimes. With the help of a computational experiment in MATLAB, a search for limit cycles and an analysis of multistability were carried out. Results. We studied dynamic scenarios for a system of three competing species for different coefficients of growth and interaction. For several combinations of parameters in a computational experiment, new continuous families of limit cycles (extreme multistability) are found. We establish bistability: the coexistence of isolated limit cycles, as well as a stationary solution and an oscillatory regime. Conclusion. We found two scenarios for locating a family of limit cycles regarding a plane passing through three equilibria corresponding to the existence of only one species. Besides cycles lying in this plane, a family is possible with cycles intersecting this plane at two points. We can consider this case as an example of periodic processes leading to overpopulation and a subsequent decline in numbers. These results will further serve as the basis for the analysis of systems of competing populations in spatially heterogeneous areas.
{"title":"Mathematical model of three competing populations and multistability of periodic regimes","authors":"Buu Hoang Nguyen, V. Tsybulin","doi":"10.18500/0869-6632-003038","DOIUrl":"https://doi.org/10.18500/0869-6632-003038","url":null,"abstract":"Purpose of this work is to analyze oscillatory regimes in a system of nonlinear differential equations describing the competition of three non-antagonistic species in a spatially homogeneous domain. Methods. Using the theory of cosymmetry, we establish a connection between the destruction of a two-parameter family of equilibria and the emergence of a continuous family of periodic regimes. With the help of a computational experiment in MATLAB, a search for limit cycles and an analysis of multistability were carried out. Results. We studied dynamic scenarios for a system of three competing species for different coefficients of growth and interaction. For several combinations of parameters in a computational experiment, new continuous families of limit cycles (extreme multistability) are found. We establish bistability: the coexistence of isolated limit cycles, as well as a stationary solution and an oscillatory regime. Conclusion. We found two scenarios for locating a family of limit cycles regarding a plane passing through three equilibria corresponding to the existence of only one species. Besides cycles lying in this plane, a family is possible with cycles intersecting this plane at two points. We can consider this case as an example of periodic processes leading to overpopulation and a subsequent decline in numbers. These results will further serve as the basis for the analysis of systems of competing populations in spatially heterogeneous areas.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78376399","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 : 2023-01-01DOI: 10.18500/0869-6632-003028
I. Soloviev, V. Klinshov
Purpose of the work is the detailed study of the attractors of the Hopfield network and their basins of attraction depending on the parameters of the system, the size of the network and the number of stored images. To characterize the basins of attraction we used the method of the so-called stability threshold, i.e., the minimum distance from an attractor to the boundary of its basin of attraction. For useful attractors, this value corresponds to the minimum distortion of the stored image, after which the system is unable to recognize it. In the result of the study it is shown that the dependence of the average stability threshold of useful attractors on the number of stored images can be nonmonotonic, due to which the stability of the network can improve when new images are memorized. An analysis of the stability thresholds allowed to estimate the maximum number of images that the network can store without fatal errors in their recognition. In this case, the stability threshold of useful attractors turns out to be close to the minimum possible value, that is, to unity. To conclude, calculation of the stability thresholds provides important information about the attraction basins of the network attractors.
{"title":"Stability thresholds of attractors of the Hopfield network","authors":"I. Soloviev, V. Klinshov","doi":"10.18500/0869-6632-003028","DOIUrl":"https://doi.org/10.18500/0869-6632-003028","url":null,"abstract":"Purpose of the work is the detailed study of the attractors of the Hopfield network and their basins of attraction depending on the parameters of the system, the size of the network and the number of stored images. To characterize the basins of attraction we used the method of the so-called stability threshold, i.e., the minimum distance from an attractor to the boundary of its basin of attraction. For useful attractors, this value corresponds to the minimum distortion of the stored image, after which the system is unable to recognize it. In the result of the study it is shown that the dependence of the average stability threshold of useful attractors on the number of stored images can be nonmonotonic, due to which the stability of the network can improve when new images are memorized. An analysis of the stability thresholds allowed to estimate the maximum number of images that the network can store without fatal errors in their recognition. In this case, the stability threshold of useful attractors turns out to be close to the minimum possible value, that is, to unity. To conclude, calculation of the stability thresholds provides important information about the attraction basins of the network attractors.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78480877","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 : 2023-01-01DOI: 10.18500/0869-6632-003030
E. Kurilova, M. Kulakov, E. Frisman
The purpose is to study the periodic regimes of the dynamics for two non-identical predator– prey communities coupled by migrations, associated with the partial synchronization of fluctuations in the abundance of communities. The combination of fluctuations in neighboring sites leads to the regimes that include both fast bursts (bursting oscillations) and slow oscillations (tonic spiking). These types of activity are characterized by a different ratio of synchronous and non-synchronous dynamics of communities in certain periods of time. In this paper, we describe scenarios of the transition between different types of burst activity. These types of dynamics differ from each other not so much in size, shape, and number of spikes in a burst, but in the order of these bursts relative to the slow-fast cycle. Methods. To study the proposed model, we use the bifurcation analysis methods of dynamic systems, as well as geometric methods based on the division of the full system into fast and slow equations (subsystems). Results. We showed that the dynamics of the first subsystem with a slow-fast limit cycle directly determines the dynamics of the second one with burst activity through a smooth dependence of regime on the number of predators and a non-smooth dependence on the number of prey. We constructed the invariant manifolds on which there are parts of dynamics with tonic (slow manifold) and burst (fast manifold) activity of the full system. Conclusion. We described the scenario for bursting with different waveforms, which are determined by the appearance of the fast invariant manifold and the location of its parts relative to the slow-fast cycle. The transitions between different types of burst are accompanied by a change in the oscillation period, the degree of synchronization, and, as a result, the dynamics becomes quasi-periodic when both communities are not synchronous with each other.
{"title":"Mechanisms leading to bursting oscillations in the system of predator–prey communities coupled by migrations","authors":"E. Kurilova, M. Kulakov, E. Frisman","doi":"10.18500/0869-6632-003030","DOIUrl":"https://doi.org/10.18500/0869-6632-003030","url":null,"abstract":"The purpose is to study the periodic regimes of the dynamics for two non-identical predator– prey communities coupled by migrations, associated with the partial synchronization of fluctuations in the abundance of communities. The combination of fluctuations in neighboring sites leads to the regimes that include both fast bursts (bursting oscillations) and slow oscillations (tonic spiking). These types of activity are characterized by a different ratio of synchronous and non-synchronous dynamics of communities in certain periods of time. In this paper, we describe scenarios of the transition between different types of burst activity. These types of dynamics differ from each other not so much in size, shape, and number of spikes in a burst, but in the order of these bursts relative to the slow-fast cycle. Methods. To study the proposed model, we use the bifurcation analysis methods of dynamic systems, as well as geometric methods based on the division of the full system into fast and slow equations (subsystems). Results. We showed that the dynamics of the first subsystem with a slow-fast limit cycle directly determines the dynamics of the second one with burst activity through a smooth dependence of regime on the number of predators and a non-smooth dependence on the number of prey. We constructed the invariant manifolds on which there are parts of dynamics with tonic (slow manifold) and burst (fast manifold) activity of the full system. Conclusion. We described the scenario for bursting with different waveforms, which are determined by the appearance of the fast invariant manifold and the location of its parts relative to the slow-fast cycle. The transitions between different types of burst are accompanied by a change in the oscillation period, the degree of synchronization, and, as a result, the dynamics becomes quasi-periodic when both communities are not synchronous with each other.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76007930","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 : 2023-01-01DOI: 10.18500/0869-6632-003043
M. Krivonosov, S. Tikhomirov
Purpose of this work is to determine the average time to reach the boundaries, as well as to identify the strategy in the game between two players, controlling point movements on the finite square lattice using an independent choice of strategies. One player wants to survive, i. e., to stay within the interior of the square, as long as possible, while his opponent wants to reach the absorbing boundary. A game starts from the center of the square and every next movement of the point is determined by independent strategy choices made by the players. The value of the game is the survival time that is the number of steps before the absorption happens. In addition we present series of experiments involving both human players and an autonomous agent (bot) and analysis of the survival time probability distributions. Methods. In this work, methods of the theory of absorbing Markov chains were used to analyze strategies and absorption times, as well as the Monte Carlo method to simulate trajectories. Additionally, a large-scale field experiment was conducted using the developed mobile application. Results. The players’ strategies are experimentally obtained for the cases of playing against an autonomous agent (bot), as well as human players against each other. A comparison with optimal strategies and a random walk is made: the difference between the experimental strategies and the optimal ones is shown, however, the resulting strategies show a much better result of games than a simple random walk. In addition, especially long-running games do not show the Markovian property in case of the simulation corresponding strategies. Conclusion. The sampled histograms indicate that the game-driven walks are more complex than a random walk on a finite lattice but it can be reproduced with a Markov Chain model.
{"title":"Strategies and first-absorption times in the random walk game","authors":"M. Krivonosov, S. Tikhomirov","doi":"10.18500/0869-6632-003043","DOIUrl":"https://doi.org/10.18500/0869-6632-003043","url":null,"abstract":"Purpose of this work is to determine the average time to reach the boundaries, as well as to identify the strategy in the game between two players, controlling point movements on the finite square lattice using an independent choice of strategies. One player wants to survive, i. e., to stay within the interior of the square, as long as possible, while his opponent wants to reach the absorbing boundary. A game starts from the center of the square and every next movement of the point is determined by independent strategy choices made by the players. The value of the game is the survival time that is the number of steps before the absorption happens. In addition we present series of experiments involving both human players and an autonomous agent (bot) and analysis of the survival time probability distributions. Methods. In this work, methods of the theory of absorbing Markov chains were used to analyze strategies and absorption times, as well as the Monte Carlo method to simulate trajectories. Additionally, a large-scale field experiment was conducted using the developed mobile application. Results. The players’ strategies are experimentally obtained for the cases of playing against an autonomous agent (bot), as well as human players against each other. A comparison with optimal strategies and a random walk is made: the difference between the experimental strategies and the optimal ones is shown, however, the resulting strategies show a much better result of games than a simple random walk. In addition, especially long-running games do not show the Markovian property in case of the simulation corresponding strategies. Conclusion. The sampled histograms indicate that the game-driven walks are more complex than a random walk on a finite lattice but it can be reproduced with a Markov Chain model.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80116117","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 : 2023-01-01DOI: 10.18500/0869-6632-003032
M. Seleznev, Y. Nikulin, Y. Khivintsev, S. Vysotskii, A. Kozhevnikov, V. Sakharov, G. Dudko, Y. Filimonov
The purpose of this work is to study the influence of four-magnon (4M) parametric instability on spin pumping by dipole-exchange magnetostatic surface waves (MSSW) with the help of the inverse spin Hall effect (ISHE) in structures based on yttrium-iron garnet (YIG) and platinum (Pt). Methods. The experiments were carried out using the delay line structures based on YIG(900 nm)/Pt(9 nm) where electromotive force (EMF) induced by ISHE demonstrates a growth at the frequencies of the resonant interaction between MSSW and volume exchange modes. The frequency dependencies of the amplitude and phase for the delay line structure and EMF (𝑈(𝑓)) from the platinum layer were studied as a function of the MSSW power. Results. It was shown that the resonant EMF growth at the frequencies of dipole-exchange resonances is caused by the presence of Van Hove singularities in the density of states for spin waves at such frequencies that leads to an increase in the efficiency of electron-magnon scattering at the YIG–Pt interface. A growth in MSSW power beyond the threshold of 4M instability development results in a “smoothing” of resonant particularities in the EMF frequency dependence 𝑈(𝑓) that can be explained by decreasing efficiency of spin pumping due to destruction of dipole-exchange resonances and related singularities in the density of states of spin waves. Conclusion. Obtained results may be of interest for the development of highly sensitive spin current detectors, as well as for the implementation of spintronic devices.
{"title":"Influence of parametric instability on spin pumping by dipole-exchange magnetostatic surface waves in YIG–Pt structures","authors":"M. Seleznev, Y. Nikulin, Y. Khivintsev, S. Vysotskii, A. Kozhevnikov, V. Sakharov, G. Dudko, Y. Filimonov","doi":"10.18500/0869-6632-003032","DOIUrl":"https://doi.org/10.18500/0869-6632-003032","url":null,"abstract":"The purpose of this work is to study the influence of four-magnon (4M) parametric instability on spin pumping by dipole-exchange magnetostatic surface waves (MSSW) with the help of the inverse spin Hall effect (ISHE) in structures based on yttrium-iron garnet (YIG) and platinum (Pt). Methods. The experiments were carried out using the delay line structures based on YIG(900 nm)/Pt(9 nm) where electromotive force (EMF) induced by ISHE demonstrates a growth at the frequencies of the resonant interaction between MSSW and volume exchange modes. The frequency dependencies of the amplitude and phase for the delay line structure and EMF (𝑈(𝑓)) from the platinum layer were studied as a function of the MSSW power. Results. It was shown that the resonant EMF growth at the frequencies of dipole-exchange resonances is caused by the presence of Van Hove singularities in the density of states for spin waves at such frequencies that leads to an increase in the efficiency of electron-magnon scattering at the YIG–Pt interface. A growth in MSSW power beyond the threshold of 4M instability development results in a “smoothing” of resonant particularities in the EMF frequency dependence 𝑈(𝑓) that can be explained by decreasing efficiency of spin pumping due to destruction of dipole-exchange resonances and related singularities in the density of states of spin waves. Conclusion. Obtained results may be of interest for the development of highly sensitive spin current detectors, as well as for the implementation of spintronic devices.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78184987","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 : 2023-01-01DOI: 10.18500/0869-6632-003054
S. Kashchenko
The subject of this work is the study of local dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings. From a discrete model describing the dynamics of a great number of coupled oscillators, a transition has been made to a nonlinear integro-differential equation, continuously depending on time and space variable. A class of full-coupled systems has been considered. The main assumption is that the amount of delay in the couplings is large enough. This assumption opens the way to the use of special asymptotic methods of study. The parameters under which the critical case is realized in the problem of the equilibrium state stability have been distinguished. It is shown that they have infinite dimension. The analogues of normal forms — nonlinear boundary value problems of Ginzburg–Landau type have been constructed. In some cases, these boundary value problems contain integral components too. Their nonlocal dynamics describes the behavior of all solutions of the original equations in the balance state neighbourhood. Methods. As applied to the considered problems, methods of constructing quasinormal forms on central manifolds are developed. An algorithm for constructing the asymptotics of solutions based on the use of quasinormal forms for determining slowly varying amplitudes has been created. Results. Quasinormal forms that determine the dynamics of the original boundary value problem have been constructed. The dominant terms of asymptotic approximations for solutions of the considered chains have been obtained. On the basis of the given statements, a number of interesting dynamical effects have been revealed. For example, an infinite alternation of direct and reverse bifurcations when the delay coefficient increases. Their distinguishing feature is that they have two or three spatial variables.
{"title":"Dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings","authors":"S. Kashchenko","doi":"10.18500/0869-6632-003054","DOIUrl":"https://doi.org/10.18500/0869-6632-003054","url":null,"abstract":"The subject of this work is the study of local dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings. From a discrete model describing the dynamics of a great number of coupled oscillators, a transition has been made to a nonlinear integro-differential equation, continuously depending on time and space variable. A class of full-coupled systems has been considered. The main assumption is that the amount of delay in the couplings is large enough. This assumption opens the way to the use of special asymptotic methods of study. The parameters under which the critical case is realized in the problem of the equilibrium state stability have been distinguished. It is shown that they have infinite dimension. The analogues of normal forms — nonlinear boundary value problems of Ginzburg–Landau type have been constructed. In some cases, these boundary value problems contain integral components too. Their nonlocal dynamics describes the behavior of all solutions of the original equations in the balance state neighbourhood. Methods. As applied to the considered problems, methods of constructing quasinormal forms on central manifolds are developed. An algorithm for constructing the asymptotics of solutions based on the use of quasinormal forms for determining slowly varying amplitudes has been created. Results. Quasinormal forms that determine the dynamics of the original boundary value problem have been constructed. The dominant terms of asymptotic approximations for solutions of the considered chains have been obtained. On the basis of the given statements, a number of interesting dynamical effects have been revealed. For example, an infinite alternation of direct and reverse bifurcations when the delay coefficient increases. Their distinguishing feature is that they have two or three spatial variables.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86727008","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 : 2023-01-01DOI: 10.18500/0869-6632-003037
Valerij Matrosov, V. Shalfeev
Purpose of this work is the research of the dynamical processes and in particular the phenomenon of the synchronization in an ensemble of coupled chaotic economic oscillators. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. The nonlinear model of economic oscillator as the system of automatic control are considered. Such kind of general economic models are unsuitable for getting some concrete economic estimations and recommendations. But such kind models are very useful for a development the theory of the economic cycles, theory of the generation, interactions, synchronization of the cycles and so on. Our numerical experiments demonstrated a good enough qualitative similarity of an chaotic economic oscillations in our model and real economic cycles. The phenomen of the synchronization of the chaotic oscillations in the ensemble of coupled economic oscillators are considered, however the accuracy of the synchronization depends with couplings essentially.
{"title":"Coupled economic oscillations — synchronization dynamical model","authors":"Valerij Matrosov, V. Shalfeev","doi":"10.18500/0869-6632-003037","DOIUrl":"https://doi.org/10.18500/0869-6632-003037","url":null,"abstract":"Purpose of this work is the research of the dynamical processes and in particular the phenomenon of the synchronization in an ensemble of coupled chaotic economic oscillators. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. The nonlinear model of economic oscillator as the system of automatic control are considered. Such kind of general economic models are unsuitable for getting some concrete economic estimations and recommendations. But such kind models are very useful for a development the theory of the economic cycles, theory of the generation, interactions, synchronization of the cycles and so on. Our numerical experiments demonstrated a good enough qualitative similarity of an chaotic economic oscillations in our model and real economic cycles. The phenomen of the synchronization of the chaotic oscillations in the ensemble of coupled economic oscillators are considered, however the accuracy of the synchronization depends with couplings essentially.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85442506","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 : 2023-01-01DOI: 10.18500/0869-6632-003022
Natalya Kovaleva, Valerij Matrosov, M. Mishchenko
Purpose of this work is to study a computational model of working memory formation based on spiking neural network with plastic connections and to study the capacity of working memory depending on the time scales of synaptic facilitation and depression and the background excitation of the network. Methods. The model imitates working memory formation within synaptic theory: memorized items are stored in form of short-term potentiated connections in selective population but not in form of persistent activity. Integrate-And-Fire neuron model in excitable mode are used as network elements. Connections between excitatory neurons demonstrates the effect of short-term plasticity. Results. It is shown that the working memory capacity increases as calcium recovery time parameter grow up or the capacity increases with neurotransmitter recovery time parameter becomes lower. Working memory capacity is found to decrease to zero with decrease of the background excitation as a result of lower values of both the mean and the variance of the external noise. Conclusion. Working memory capacity was studied as a function of time scales of synaptic facilitation and depression and background excitation of the network. Estimated working memory capacity is shown to be possibly larger than classical experimental estimations of four items. But capacity strongly depends on intrinsic parameters of neural networks
{"title":"Working memory capacity: the role of parameters of spiking neural network model","authors":"Natalya Kovaleva, Valerij Matrosov, M. Mishchenko","doi":"10.18500/0869-6632-003022","DOIUrl":"https://doi.org/10.18500/0869-6632-003022","url":null,"abstract":"Purpose of this work is to study a computational model of working memory formation based on spiking neural network with plastic connections and to study the capacity of working memory depending on the time scales of synaptic facilitation and depression and the background excitation of the network. Methods. The model imitates working memory formation within synaptic theory: memorized items are stored in form of short-term potentiated connections in selective population but not in form of persistent activity. Integrate-And-Fire neuron model in excitable mode are used as network elements. Connections between excitatory neurons demonstrates the effect of short-term plasticity. Results. It is shown that the working memory capacity increases as calcium recovery time parameter grow up or the capacity increases with neurotransmitter recovery time parameter becomes lower. Working memory capacity is found to decrease to zero with decrease of the background excitation as a result of lower values of both the mean and the variance of the external noise. Conclusion. Working memory capacity was studied as a function of time scales of synaptic facilitation and depression and background excitation of the network. Estimated working memory capacity is shown to be possibly larger than classical experimental estimations of four items. But capacity strongly depends on intrinsic parameters of neural networks","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84968343","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 : 2023-01-01DOI: 10.18500/0869-6632-003051
V. Aristov, O. Kubryak, I. Stepanyan
The purpose of the study is experimental verification of the proposed EEG analysis method based on the construction of a connectivity graph of the analyzed signal, in which the amplitudes are displayed by vertices, and their relative position relative to each other by arcs. The display of the EEG signal in the graph structure causes the appearance of cyclic structures with the possibility of calculating their numerical characteristics. As a result of the study, criteria for initialization of the initial conditions of the counting algorithm have been developed. The following parameters were calculated: the number of cycles and the Euler number in the EEG recording. Coil representations of graphs are given. The proposed algorithm has a scaling parameter, the choice of which affects the final results. The second free parameter of the proposed algorithm is the degree of artificial signal coarsening. Variants of the algorithm application for multichannel EEG signals with multichannel signal processing by channel-by-channel detection of semantic units and construction of a generalized semantic connectivity graph are considered. An example of an analyzed multichannel EEG signal, which was pre-processed with reduction of all amplitudes to natural numbers in accordance with the calculated characteristics, is given. An example of an EEG of a subject with closed eyes during quiet wakefulness and an EEG of a subject with open eyes is given. In Conclusion, it is shown that the final indicators can vary significantly (from zero to tens of thousands or more) depending on the particular derivation of the EEG channel. Analysis of the cyclic structures of the electroencephalogram seems to be a potential way to assess various human states due to the possibility of distinguishing them using the proposed method. The study has a limited, pilot character.
{"title":"Calculation of the cyclic characteristics of the electroencephalogram for investigation of the electrical activity of the brain","authors":"V. Aristov, O. Kubryak, I. Stepanyan","doi":"10.18500/0869-6632-003051","DOIUrl":"https://doi.org/10.18500/0869-6632-003051","url":null,"abstract":"The purpose of the study is experimental verification of the proposed EEG analysis method based on the construction of a connectivity graph of the analyzed signal, in which the amplitudes are displayed by vertices, and their relative position relative to each other by arcs. The display of the EEG signal in the graph structure causes the appearance of cyclic structures with the possibility of calculating their numerical characteristics. As a result of the study, criteria for initialization of the initial conditions of the counting algorithm have been developed. The following parameters were calculated: the number of cycles and the Euler number in the EEG recording. Coil representations of graphs are given. The proposed algorithm has a scaling parameter, the choice of which affects the final results. The second free parameter of the proposed algorithm is the degree of artificial signal coarsening. Variants of the algorithm application for multichannel EEG signals with multichannel signal processing by channel-by-channel detection of semantic units and construction of a generalized semantic connectivity graph are considered. An example of an analyzed multichannel EEG signal, which was pre-processed with reduction of all amplitudes to natural numbers in accordance with the calculated characteristics, is given. An example of an EEG of a subject with closed eyes during quiet wakefulness and an EEG of a subject with open eyes is given. In Conclusion, it is shown that the final indicators can vary significantly (from zero to tens of thousands or more) depending on the particular derivation of the EEG channel. Analysis of the cyclic structures of the electroencephalogram seems to be a potential way to assess various human states due to the possibility of distinguishing them using the proposed method. The study has a limited, pilot character.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76232128","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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