Influence of coupling on the dynamics of three delayed oscillators
Open Access
- 30 November 2021
- journal article
- research article
- Published by Saratov State University in Izvestiya VUZ. Applied Nonlinear Dynamics
- Vol. 29 (6), 869-891
- https://doi.org/10.18500/0869-6632-2021-29-6-869-891
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.Keywords
This publication has 12 references indexed in Scilit:
- Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of CouplingMathematics, 2020
- Relaxation modes of a system of diffusion coupled oscillators with delayCommunications in Nonlinear Science and Numerical Simulation, 2020
- Relaxation cycles in a model of two weakly coupled oscillators with sign-changing delayed feedbackTheoretical and Mathematical Physics, 2020
- Normal and quasinormal forms for systems of difference and differential-difference equationsCommunications in Nonlinear Science and Numerical Simulation, 2016
- Buffering in cyclic gene networksTheoretical and Mathematical Physics, 2016
- Model of human cardiovascular system with a loop of autonomic regulation of the mean arterial pressureJournal of the American Society of Hypertension, 2015
- An experimental digital communication scheme based on chaotic time-delay systemNonlinear Dynamics, 2013
- Large-Amplitude Periodic Solutions for Differential Equations with Delayed Monotone Positive FeedbackJournal of Dynamics and Differential Equations, 2011
- Dynamics of Nonlinear Time-Delay SystemsPublished by Springer Science and Business Media LLC ,2011
- Delay Equations with Rapidly Oscillating Stable Periodic SolutionsJournal of Dynamics and Differential Equations, 2007