Dynamics of a System of Two Simplest Oscillators with Finite Non-linear Feedbacks

Modelirovanie i Analiz Informacionnyh Sistem

A. A. Kashchenko¹ 

[1] P.G. Demidov Yaroslavl State University;

关键词: asymptotics;    stability;    large parameter;    relaxation oscillation;    periodic solution;   

DOI  :  10.18255/1818-1015-2016-6-841-849

来源: DOAJ

【 摘 要 】

In this paper, we consider a singularly perturbed system of two differential equations with delay which simulates two coupled oscillators with nonlinear feedback. Feedback function is assumed to be finite, piecewise continuous, and with a constant sign. In this paper, we prove the existence of relaxation periodic solutions and make conclusion about their stability. With the help of the special method of a large parameter we construct asymptotics of the solutions with the initial conditions of a certain class. On this asymptotics we build a special mapping, which in the main describes the dynamics of the original model. It is shown that the dynamics changes significantly with the decreasing of coupling coefficient: we have a stable homogeneous periodic solution if the coupling coefficient is of unity order, and with decreasing the coupling coefficient the dynamics become more complex, and it is described by a special mapping. It was shown that for small values of the coupling under certain values of the parameters several different stable relaxation periodic regimes coexist in the original problem.

【 授权许可】

Unknown