This article is cited in 1 scientific paper (total in 1 paper)
Dynamics of a system of two simplest oscillators with finite non-linear feedbacks
A. A. Kashchenko
P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., Yaroslavl 150003, Russia
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.
asymptotics, stability, large parameter, relaxation oscillation, periodic solution.
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A. A. Kashchenko, “Dynamics of a system of two simplest oscillators with finite non-linear feedbacks”, Model. Anal. Inform. Sist., 23:6 (2016), 841–849
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\paper Dynamics of a system of two simplest oscillators with finite non-linear feedbacks
\jour Model. Anal. Inform. Sist.
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A. A. Kaschenko, “Semeistvo negrubykh tsiklov v sisteme dvukh svyazannykh generatorov s zapazdyvaniem”, Model. i analiz inform. sistem, 24:5 (2017), 649–654
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