|
Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev
Asymptotics of Self-Oscillations in Chains of Systems
of Nonlinear Equations
Sergey A. Kashchenko Regional Scientific and Educational Mathematical Center of the Yaroslavl State University,
ul. Sovetskaya 14, 150003 Yaroslavl, Russia
Abstract:
We study the local dynamics of chains of coupled nonlinear systems of second-
order ordinary differential equations of diffusion-difference type. The main assumption is that
the number of elements of chains is large enough. This condition allows us to pass to the
problem with a continuous spatial variable. Critical cases have been considered while studying
the stability of the equilibrum state. It is shown that all these cases have infinite dimension.
The research technique is based on the development and application of special methods for
construction of normal forms. Among the main results of the paper, we include the creation of
new nonlinear boundary value problems of parabolic type, whose nonlocal dynamics describes
the local behavior of solutions of the original system.
Keywords:
self-oscillations, dynamics, stability, coupled chains, asymptotic behavior
Received: 29.08.2023 Accepted: 15.01.2024
Citation:
Sergey A. Kashchenko
Linking options:
https://www.mathnet.ru/eng/rcd1255
|
Statistics & downloads: |
Abstract page: | 36 | References: | 16 |
|