Pub Date : 2021-11-30DOI: 10.18500/0869-6632-2021-29-6-869-891
A. Kashchenko
The purpose of this study is to construct the asymptotics of the relaxation regimes of a system of differential equations with delay, which simulates three diffusion-coupled oscillators with nonlinear compactly supported delayed feedback under the assumption that the factor in front of the feedback function is large enough. Also, the purpose is to study the influence of the coupling between the oscillators on the nonlocal dynamics of the model. Methods. We construct the asymptotics of solutions of the considered model with initial conditions from a special set. From the asymptotics of the solutions, we obtain an operator of the translation along the trajectories that transforms the set of initial functions into a set of the same type. The main part of this operator is described by a finite-dimensional mapping. The study of its dynamics makes it possible to refine the asymptotics of the solutions of the original model and draw conclusions about its dynamics. Results. It follows from the form of the constructed mapping that for positive coupling parameters of the original model, starting from a certain moment of time, all three generators have the same main part of the asymptotics — the generators are “synchronized”. At negative values of the coupling parameter, both inhomogeneous relaxation cycles and irregular regimes are possible. The connection of these modes with the modes of the constructed finite-dimensional mapping is described. Conclusion. From the results of the work it follows that the dynamics of the model under consideration is fundamentally influenced by the value of the coupling parameter between the generators.
{"title":"Influence of coupling on the dynamics of three delayed oscillators","authors":"A. Kashchenko","doi":"10.18500/0869-6632-2021-29-6-869-891","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-6-869-891","url":null,"abstract":"The purpose of this study is to construct the asymptotics of the relaxation regimes of a system of differential equations with delay, which simulates three diffusion-coupled oscillators with nonlinear compactly supported delayed feedback under the assumption that the factor in front of the feedback function is large enough. Also, the purpose is to study the influence of the coupling between the oscillators on the nonlocal dynamics of the model. Methods. We construct the asymptotics of solutions of the considered model with initial conditions from a special set. From the asymptotics of the solutions, we obtain an operator of the translation along the trajectories that transforms the set of initial functions into a set of the same type. The main part of this operator is described by a finite-dimensional mapping. The study of its dynamics makes it possible to refine the asymptotics of the solutions of the original model and draw conclusions about its dynamics. Results. It follows from the form of the constructed mapping that for positive coupling parameters of the original model, starting from a certain moment of time, all three generators have the same main part of the asymptotics — the generators are “synchronized”. At negative values of the coupling parameter, both inhomogeneous relaxation cycles and irregular regimes are possible. The connection of these modes with the modes of the constructed finite-dimensional mapping is described. Conclusion. From the results of the work it follows that the dynamics of the model under consideration is fundamentally influenced by the value of the coupling parameter between the generators.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81070229","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 : 2021-11-30DOI: 10.18500/0869-6632-2021-29-6-833-834
I. Sysoev
{"title":"Nonlinear days in Saratov for young scientists","authors":"I. Sysoev","doi":"10.18500/0869-6632-2021-29-6-833-834","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-6-833-834","url":null,"abstract":"","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88529965","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 : 2021-11-30DOI: 10.18500/0869-6632-2021-29-6-943-952
V. Nechaev, E. Rybalova, G. Strelkova
The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods. In this paper, snapshots of the system dynamics are constructed for various values of the parameters, as well as spatial distributions of cross-correlation coefficient values, which enable us to determine the regime observed in the system for these parameters. To improve the accuracy of the obtained results, the numerical studies are carried out for fifty different realizations of initial conditions of the ring elements. Results. It is shown that a fixed inhomogeneous distribution of the control parameters with increasing noise intensity leads to an increase in the range of the coupling strength where chimera states are observed. With this, the boundary lying in the region of strong coupling changes more significantly as compared with the case of weak coupling strength. The opposite effect is provided when the control parameters are permanently affected by noise. In this case increasing the noise intensity leads to a decrease in the interval of existence of chimera states. Additionally, the nature of the random variable distribution (normal or uniform one) does not strongly influence the observed changes in the ring dynamics. The regions of existence of chimera states are constructed in the plane of «coupling strength – noise intensity» parameters. Conclusion. We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used. It has been shown that in order to increase the region of observing chimera states, the control parameters of the elements must be distributed inhomogeneously over the entire ensemble. To reduce this region, a constant noise effect on the control parameters should be used.
{"title":"Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps","authors":"V. Nechaev, E. Rybalova, G. Strelkova","doi":"10.18500/0869-6632-2021-29-6-943-952","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-6-943-952","url":null,"abstract":"The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods. In this paper, snapshots of the system dynamics are constructed for various values of the parameters, as well as spatial distributions of cross-correlation coefficient values, which enable us to determine the regime observed in the system for these parameters. To improve the accuracy of the obtained results, the numerical studies are carried out for fifty different realizations of initial conditions of the ring elements. Results. It is shown that a fixed inhomogeneous distribution of the control parameters with increasing noise intensity leads to an increase in the range of the coupling strength where chimera states are observed. With this, the boundary lying in the region of strong coupling changes more significantly as compared with the case of weak coupling strength. The opposite effect is provided when the control parameters are permanently affected by noise. In this case increasing the noise intensity leads to a decrease in the interval of existence of chimera states. Additionally, the nature of the random variable distribution (normal or uniform one) does not strongly influence the observed changes in the ring dynamics. The regions of existence of chimera states are constructed in the plane of «coupling strength – noise intensity» parameters. Conclusion. We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used. It has been shown that in order to increase the region of observing chimera states, the control parameters of the elements must be distributed inhomogeneously over the entire ensemble. To reduce this region, a constant noise effect on the control parameters should be used.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82654967","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 : 2021-11-30DOI: 10.18500/0869-6632-2021-29-6-915-926
V. Muchkaev, A. Onishchenko, V. Tsarev
Purpose of this work is to study modes and conditions that make it possible to excite the highest type of microwave oscillations, the frequency of which is a multiple of the frequency of the main type, in a monotron with a three-band resonator. Method of the investigation is a numerical 3D modeling, used to calculate the dimensions and electrodynamic parameters of the resonator (characteristic impedance, coupling coefficient, relative electronic conductivity); operation modes of the monotron are considered, which are characterized by excitation of oscillations in the highest type oscillations. Result. In the resonator under consideration, it is possible to achieve a multiple (equal to three) ratio between the frequency of the 25th highest type of oscillations and the frequency of the π/2-type. It was shown that in such resonator simultaneous excitation of electromagnetic field on those frequencies can be made. The maximum of an output power achieved at 100.22 GHz is 15.4 W with an accelerating voltage of 7825 V and an electronic beam microperveance 0.36 µA/V3/2 . The maximal efficiency on a third harmonic is 0.83% while the total efficiency (generating electromagnetic waves of the first and the third harmonics) is up to 17%. Conclusion. It was set that the described method of generation of terahertz range radiation is promising for further investigation, as it solves problem that orthodox microwave devices meet in the millimeter wavelength range, such as small linear dimensions of the components and critical current density of the electronic beam.
{"title":"Generation of double-frequency radiation in monotron with three-gap cavity","authors":"V. Muchkaev, A. Onishchenko, V. Tsarev","doi":"10.18500/0869-6632-2021-29-6-915-926","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-6-915-926","url":null,"abstract":"Purpose of this work is to study modes and conditions that make it possible to excite the highest type of microwave oscillations, the frequency of which is a multiple of the frequency of the main type, in a monotron with a three-band resonator. Method of the investigation is a numerical 3D modeling, used to calculate the dimensions and electrodynamic parameters of the resonator (characteristic impedance, coupling coefficient, relative electronic conductivity); operation modes of the monotron are considered, which are characterized by excitation of oscillations in the highest type oscillations. Result. In the resonator under consideration, it is possible to achieve a multiple (equal to three) ratio between the frequency of the 25th highest type of oscillations and the frequency of the π/2-type. It was shown that in such resonator simultaneous excitation of electromagnetic field on those frequencies can be made. The maximum of an output power achieved at 100.22 GHz is 15.4 W with an accelerating voltage of 7825 V and an electronic beam microperveance 0.36 µA/V3/2 . The maximal efficiency on a third harmonic is 0.83% while the total efficiency (generating electromagnetic waves of the first and the third harmonics) is up to 17%. Conclusion. It was set that the described method of generation of terahertz range radiation is promising for further investigation, as it solves problem that orthodox microwave devices meet in the millimeter wavelength range, such as small linear dimensions of the components and critical current density of the electronic beam.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75968370","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 : 2021-11-30DOI: 10.18500/0869-6632-2021-29-6-927-942
N. Egorov, V. Ponomarenko, S. Melnikova, I. Sysoev, M. Sysoeva
This work aims to show that long transient processes in mesascale models of thalamocortical brain network can appear in very general case, in particular for different number of elements in the ensemble (different level of detalization) and different initial phase of external driving, with these regimes surviving at small variations of number and structure of couplings. Methods. Thalamocortical brain networks are modelled using electronic circuit realized using computer SPICE eluating software. FitzHugh – Nagumo analog generator is used as a single circuit element. Results. Long quasiregular and nonregular oscillation processes with stationary amplitude were shown to occur in ensembles of 14, 28 and 56 model FitzHug – Nagumo generators. The dependency of transient process length on the external driving initial phase and particular coupling matrix structure was studied. Conclusion. The proposed electronic models of thalamocortical system were proved to reproduce the pathological regimes of brain activity in similar way despite the number of elements in the circuit, connectivity matrix and initial driving phase.
{"title":"Common mechanisms of attractorless oscillatory regimes in radioengineering models of brain thalamocortical network","authors":"N. Egorov, V. Ponomarenko, S. Melnikova, I. Sysoev, M. Sysoeva","doi":"10.18500/0869-6632-2021-29-6-927-942","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-6-927-942","url":null,"abstract":"This work aims to show that long transient processes in mesascale models of thalamocortical brain network can appear in very general case, in particular for different number of elements in the ensemble (different level of detalization) and different initial phase of external driving, with these regimes surviving at small variations of number and structure of couplings. Methods. Thalamocortical brain networks are modelled using electronic circuit realized using computer SPICE eluating software. FitzHugh – Nagumo analog generator is used as a single circuit element. Results. Long quasiregular and nonregular oscillation processes with stationary amplitude were shown to occur in ensembles of 14, 28 and 56 model FitzHug – Nagumo generators. The dependency of transient process length on the external driving initial phase and particular coupling matrix structure was studied. Conclusion. The proposed electronic models of thalamocortical system were proved to reproduce the pathological regimes of brain activity in similar way despite the number of elements in the circuit, connectivity matrix and initial driving phase.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87770886","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 : 2021-09-30DOI: 10.18500/0869-6632-2021-29-5-739-750
A. Alifov
The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs. This is especially important from the point of view of calculations when designing real devices. Results. The characteristic of the friction force that causes self-oscillations, represented by a general polynomial function, is linearized using the method of direct linearization of nonlinearities. Using the same method, solutions of the differential equations of motion of the system are constructed, equations are obtained for determining the nonstationary values of the amplitude, phase of oscillations and the speed of the energy source. Stationary motions are considered, as well as their stability by means of the Routh–Hurwitz criteria. Performed calculations obtained information about the effect of delays on the dynamics of the system. Conclusion. Calculations have shown that delays shift the amplitude curves to the right and left, up and down on the amplitude–frequency plane, change their shape, and affect the stability of motion.
{"title":"Mixed forced, parametric, and self-oscillations with nonideal energy source and lagging forces","authors":"A. Alifov","doi":"10.18500/0869-6632-2021-29-5-739-750","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-5-739-750","url":null,"abstract":"The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs. This is especially important from the point of view of calculations when designing real devices. Results. The characteristic of the friction force that causes self-oscillations, represented by a general polynomial function, is linearized using the method of direct linearization of nonlinearities. Using the same method, solutions of the differential equations of motion of the system are constructed, equations are obtained for determining the nonstationary values of the amplitude, phase of oscillations and the speed of the energy source. Stationary motions are considered, as well as their stability by means of the Routh–Hurwitz criteria. Performed calculations obtained information about the effect of delays on the dynamics of the system. Conclusion. Calculations have shown that delays shift the amplitude curves to the right and left, up and down on the amplitude–frequency plane, change their shape, and affect the stability of motion.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80674521","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 : 2021-09-30DOI: 10.18500/0869-6632-2021-29-5-812-828
A. Kozhevnikov, G. Dudko, Y. Khivintsev, V. Sakharov, S. Vysotskii, Y. Nikulin, Michael Seleznev, Aleksander Khitun, Y. Filimonov
Subject. A change in the spectrum of spin waves (SW) in a magnetic cross is investigated when two signals pass through it: a pump signal and a probe signal. Objective. Detection of specific features in formation of the spectra of the output signals of SW in the multiport structure based on a yttrium iron garnet (YIG) film in the case of excitation of two magnetostatic surface waves (MSSW) simultaneously by the input antenna, where the first, with power higher than the first-order parametric instability threshold is the pump, and the second one is a probe. Methods. The experiments were performed for a cross structure from YIG film in the form of two orthogonal waveguides with the SW wire antennas placed at the ends of the waveguides, where one of the antennas on the transversely magnetized waveguide was considered as the input. Result. It was found that by choosing the probing signal frequency, one can significantly (by 10 dB) change the relative signal levels for the satellite waves at the output antennas, which are secondary MSSWs with some new frequencies and appear in the output signals spectrum as a result of the thresholdless processes of merging of parametric spin waves generated by MSSW pumping. In this case the secondary MSSWs frequencies can differ at the output antennas located on orthogonal waveguides. Discussion. The discovered effect is associated with the nonreciprocal nature of propagation of both the pumping wave and the waves generated at parametric instability condition in the structure.
{"title":"Effect of probing signal on the output signals spectrum of nonlinear spin waves in a cross based on waveguides of iron-yttrium garnet film","authors":"A. Kozhevnikov, G. Dudko, Y. Khivintsev, V. Sakharov, S. Vysotskii, Y. Nikulin, Michael Seleznev, Aleksander Khitun, Y. Filimonov","doi":"10.18500/0869-6632-2021-29-5-812-828","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-5-812-828","url":null,"abstract":"Subject. A change in the spectrum of spin waves (SW) in a magnetic cross is investigated when two signals pass through it: a pump signal and a probe signal. Objective. Detection of specific features in formation of the spectra of the output signals of SW in the multiport structure based on a yttrium iron garnet (YIG) film in the case of excitation of two magnetostatic surface waves (MSSW) simultaneously by the input antenna, where the first, with power higher than the first-order parametric instability threshold is the pump, and the second one is a probe. Methods. The experiments were performed for a cross structure from YIG film in the form of two orthogonal waveguides with the SW wire antennas placed at the ends of the waveguides, where one of the antennas on the transversely magnetized waveguide was considered as the input. Result. It was found that by choosing the probing signal frequency, one can significantly (by 10 dB) change the relative signal levels for the satellite waves at the output antennas, which are secondary MSSWs with some new frequencies and appear in the output signals spectrum as a result of the thresholdless processes of merging of parametric spin waves generated by MSSW pumping. In this case the secondary MSSWs frequencies can differ at the output antennas located on orthogonal waveguides. Discussion. The discovered effect is associated with the nonreciprocal nature of propagation of both the pumping wave and the waves generated at parametric instability condition in the structure.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89327133","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 : 2021-09-30DOI: 10.18500/0869-6632-2021-29-5-751-764
V. Tsybulin, T. D. Ha, P. Zelenchuk
The purpose of this work is to study the influence of various local models in the equations of diffusion–advection– reaction on the spatial processes of coexistence of predators and prey under conditions of a nonuniform distribution of the carrying capacity. We consider a system of nonlinear parabolic equations to describe diffusion, taxis, and local interaction of a predator and prey in a one-dimensional habitat. Methods. We carried out the study of the system using the dynamical systems approach and a computational experiment based on the method of lines and a scheme of staggered grids. Results. The behavior of the predator – prey system has been studied for various scenarios of local interaction, taking into account the hyperbolic law of prey growth and the Holling effect with nonuniform carrying capacity. We have established paradoxical scenarios of interaction between prey and predator for several modifications of the trophic function. Stationary and nonstationary solutions are analyzed considering diffusion and directed migration of species. Conclusion. The trophic function that considers the heterogeneity of the resource is proposed, which does not lead to paradoxical dynamics.
{"title":"Nonlinear dynamics of the predator – prey system in a heterogeneous habitat and scenarios of local interaction of species","authors":"V. Tsybulin, T. D. Ha, P. Zelenchuk","doi":"10.18500/0869-6632-2021-29-5-751-764","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-5-751-764","url":null,"abstract":"The purpose of this work is to study the influence of various local models in the equations of diffusion–advection– reaction on the spatial processes of coexistence of predators and prey under conditions of a nonuniform distribution of the carrying capacity. We consider a system of nonlinear parabolic equations to describe diffusion, taxis, and local interaction of a predator and prey in a one-dimensional habitat. Methods. We carried out the study of the system using the dynamical systems approach and a computational experiment based on the method of lines and a scheme of staggered grids. Results. The behavior of the predator – prey system has been studied for various scenarios of local interaction, taking into account the hyperbolic law of prey growth and the Holling effect with nonuniform carrying capacity. We have established paradoxical scenarios of interaction between prey and predator for several modifications of the trophic function. Stationary and nonstationary solutions are analyzed considering diffusion and directed migration of species. Conclusion. The trophic function that considers the heterogeneity of the resource is proposed, which does not lead to paradoxical dynamics.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77006286","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 : 2021-09-30DOI: 10.18500/0869-6632-2021-29-5-765-774
A. Funtov
Purpose of this work is to construct a theory of extended interaction klystron with ordinary distributed resonators, but with a drift space in the form of medium with complex permittivity. Methods. For this, a hybrid of extended interaction klystron and an amplifier with a complex permittivity is considered in the framework of the weak signal approximation. Two types of configurations of a extended interaction klystron were considered: with two and three distributed resonators. For a two-resonator klystron with distributed interaction, two cases are considered: without reflections from the ends of distributed resonators and the case when the input binder is fully matched to the external transmission line, and for the second distributed resonator, the so-called condition of critical coupling of the “hot” resonator with the transmission line is satisfied. For a three-resonator klystron with distributed interaction, the case is considered without reflections from the ends of distributed resonators. Results and conclusion. According to the results of the developed theory of a weak signal in a extended interaction klystron with ordinary distributed resonators and a drift space with a complex dielectric constant, by choosing the parameters, it is possible to achieve a greater gain at a length that is shorter than in a conventional extended interaction klystron, all other things being equal. In addition, the presence of an intermediate distributed resonator makes it possible to increase the gain while maintaining the full length of the device.
{"title":"About theory of extended interaction klystron and drift space in the form of medium with complex permittivity","authors":"A. Funtov","doi":"10.18500/0869-6632-2021-29-5-765-774","DOIUrl":"https://doi.org/10.18500/0869-6632-2021-29-5-765-774","url":null,"abstract":"Purpose of this work is to construct a theory of extended interaction klystron with ordinary distributed resonators, but with a drift space in the form of medium with complex permittivity. Methods. For this, a hybrid of extended interaction klystron and an amplifier with a complex permittivity is considered in the framework of the weak signal approximation. Two types of configurations of a extended interaction klystron were considered: with two and three distributed resonators. For a two-resonator klystron with distributed interaction, two cases are considered: without reflections from the ends of distributed resonators and the case when the input binder is fully matched to the external transmission line, and for the second distributed resonator, the so-called condition of critical coupling of the “hot” resonator with the transmission line is satisfied. For a three-resonator klystron with distributed interaction, the case is considered without reflections from the ends of distributed resonators. Results and conclusion. According to the results of the developed theory of a weak signal in a extended interaction klystron with ordinary distributed resonators and a drift space with a complex dielectric constant, by choosing the parameters, it is possible to achieve a greater gain at a length that is shorter than in a conventional extended interaction klystron, all other things being equal. In addition, the presence of an intermediate distributed resonator makes it possible to increase the gain while maintaining the full length of the device.","PeriodicalId":41611,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74147465","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 : 2021-09-30DOI: 10.18500/0869-6632-2021-29-5-727-738
Y. Morozov
Most of intracavity pumped optical parametric oscillators (OPO) are made nowaday according to a scheme with a single-resonance OPO located in the cavity of a pump laser. Usually the cavities of the pump and OPO (signal) emission have different values of round-trip time (delay). Aim of the study is therefore to build up the mathematical model of intracavity optical parametric oscillator (ICOPO) considered as a time-delay dynamic system with two values of delay in both cavities (the pump and signal). Methods. The model allows to analyze the steady state (equilibrium point) of the dynamic system and its stability with the help of characteristic equation’s solution. Results. Countless set of the characteristic equation roots is shown to consist of complex-conjugate pairs with imaginary parts which are nearly multiples of intermode beat frequencies in the pump and signal cavities. The diagram of stability depending on the position of nonlinear crystal in the resonator was built on the parameter plane. Features of the plane partition into the areas of stability/instabilty vs behavior of the characteristic equation roots are examined. Discussion. The results of the study allow to consider an ICOPO as the time-delay dynamic system thus adding to the physical picture of intracavity parametric oscillators.
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