卷 31, 编号 3 (2023)
Articles
70 years of Sergey V. Gonchenko
摘要
May 10, 2023 marks the 70th birthday of Professor Sergey Vladimirovich Gonchenko, a leading researcher of Lobachevsky State University of Nizhny Novgorod.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):247-248
247-248
40 years of Ilya V. Sysoev
摘要
June 9, 2023 marks the 40th anniversary of the vice editor-in-chief of the journal "Izvestiya VUZ. AND", Ph.D., Professor of SGU Ilya Vyacheslavovich Sysoev.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):249-253
249-253
Coupled economic oscillations — synchronization dynamical model
摘要
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.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):254-270
254-270
Spatial and temporal dynamics of the emergence of epidemics in the hybrid SIRS+V model of cellular automata
摘要
Purpose of this work is to construct a model of infection spread in the form of a lattice of probabilistic cellular automata, which takes into account the inertial nature of infection transmission between individuals. Identification of the relationship between the spatial and temporal dynamics of the model depending on the probability of migration of individuals. Methods. The numerical simulation of stochastic dynamics of the lattice of cellular automata by the Monte Carlo method. Results. A modified SIRS+V model of epidemic spread in the form of a lattice of probabilistic cellular automata is constructed. It differs from standard models by taking into account the inertial nature of the transmission of infection between individuals of the population, which is realized by introducing a "carrier agent" into the model, which viruses act as. The similarity and difference between the dynamics of the cellular automata model and the previously studied mean field model are revealed. Discussion. The model in the form of cellular automata allows us to study the processes of infection spread in the population, including in conditions of spatially heterogeneous distribution of the disease. The latter situation occurs if the probability of migration of individuals is not too high. At the same time, a significant change in the quantitative characteristics of the processes is possible, as well as the emergence of qualitatively new modes, such as the regime of undamped oscillations.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):271-285
271-285
Transfer of passive particles in the velocity field of vortex tripole moving on a plane
摘要
Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):286-304
286-304
Application of joint singularity spectrum to analyze cooperative dynamics of complex systems
摘要
Purpose of this work is to generalize the wavelet-transform modulus maxima method to the case of cooperative dynamics of interacting systems and to introduce the joint singularity spectrum into consideration. The research method is the wavelet-based multifractal formalism, the generalized version of which is used to quantitatively describe the effect of chaotic synchronization in the dynamics of model systems. Models of coupled Rossler systems and paired nephrons are considered. As a result of the studies carried out, the main changes in the joint singularity spectra were noted during the transition from synchronous to asynchronous oscillations in the first model and to the partial synchronization mode in the second model. Conclusion. Proposed approach can be used in studies of the cooperative dynamics of systems of various nature.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):305-315
305-315
Mathematical model of three competing populations and multistability of periodic regimes
摘要
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.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):316-333
316-333
Strategies and first-absorption times in the random walk game
摘要
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.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):334-350
334-350
Ambient light at night causes desynchronization of rhythms in the sleep–wake switching model
摘要
The purpose of this study is to analyze the influence of the shape of the daily illumination profile on the synchronization of rhythms in the sleep–wake state switching model. Normally, the alternation of sleep and wakefulness of a person is synchronized with his circadian rhythm and with the 24-hour rhythm of illumination. There is, however, a lot of experimental evidence of a violation of this synchronism, both in the form of phase failures (for example, during air travel) and in the form of long-term mismatch of rhythms (for example, during shift work in production). Mathematical models of the process of switching between sleep and wakefulness also demonstrate the desynchronization of rhythms and are successfully used to optimize work schedules. At the same time, the influence of a number of factors on this process has not been sufficiently studied, including the nature of changes in illumination during the day. Methods. An analysis of the six-dimensional model under study shows that, in terms of nonlinear dynamics, the problem is reduced to finding and interpreting resonance regions on a three-dimensional torus. For the specific purposes of our work, it turned out to be convenient to estimate the ratio of three periods (24 hours, the circadian period, and the current duration of the sleep–wake cycle) by numerically integrating the model equations on a grid of parameter values using parallel computing technology. The main result of our work is that the presence of round-the-clock low-intensity illumination (that is, the addition of a zero-frequency signal to the daily light cycle) causes the circadian rhythm to desynchronize with respect to the daily one in a significant range of parameters. We have proposed an explanation of this effect based on the structure of the mathematical model. Conclusion. Our results raise at least two serious questions, the first of which is related to the physiological interpretation of one of the main variables of the model, sleep homeostasis, and the second is to refine the assumptions that are used in the model description of the photoreceptor response. In any case, there are interesting prospects for further research.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):351-364
351-364
Longitudinal waves in the walls of an annular channel filled with liquid and made of a material with fractional nonlinearity
摘要
Purpose of this paper is to study the evolution of longitudinal strain waves in the walls of an annular channel filled with a viscous incompressible fluid. The walls of the channel were represented as coaxial shells with fractional physical nonlinearity. The viscosity of the fluid and its influence on the wave process was taken into account within the study. Metods. The system of two evolutionary equations, which are generalized Schamel equations, was obtained by the two-scale asymptotic expansion method. The fractional nonlinearity of the channel wall material leads to the necessity to use a computational experiment to study the wave dynamics in them. The computational experiment was conducted based on obtaining new difference schemes for the governing equations. These schemes are analogous to the Crank–Nicholson scheme for modeling heat propagation. Results. Numerical simulation showed that over time, the velocity and amplitude of the deformation waves remain unchanged, and the wave propagation direction concurs with the positive direction of the longitudinal axis. The latter specifies that the velocity of the waves is supersonic. For a particular case, the coincidence of the computational experiment with the exact solution is shown. This substantiates the adequacy of the proposed difference scheme for the generalized Schamel equations. In addition, it was shown that solitary deformation waves in the channel walls are solitons.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):365-376
365-376
To the 85th anniversary of Dmitry Ivanovich Trubetskov
摘要
On June 14, 2023, could be celebrated the 85-th anniversary of the founder of the journal “Applied Nonlinear Dynamics”, the Corresponding Member of the Russian Academy of Sciences, the Honored Scientist of the Russian Federation, the laureate of the Presidential Prize in Education, the Rector of Saratov University (1994–2003), the head of the department electronics, oscillations and waves (1981–2020) Dmitry Ivanovich Trubetskov. Published reflections of colleagues and friends of D. I. Trubetskov reveal his contribution to the development of science, education and the significance of his multifaceted personality for the history of Saratov University.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(3):377-400
377-400