Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations

    2024, Volume 29, Number 1, pp.  218-240

    Author(s): Kashchenko S. A.

    We study the local dynamics of chains of coupled nonlinear systems of secondorder 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
    Citation: Kashchenko S. A., Asymptotics of Self-Oscillations in Chains of Systems of Nonlinear Equations, Regular and Chaotic Dynamics, 2024, Volume 29, Number 1, pp. 218-240

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