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Chains with Connections of Diffusion and Advective Types

Author

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  • Sergey Kashchenko

    (Regional Scientific and Educational Mathematical Center “Centre of Integrable Systems”, P. G. Demidov Yaroslavl State University, 150003 Yaroslavl, Russia)

Abstract

The local dynamics of a system of oscillators with a large number of elements and with diffusive- and advective-type couplings containing a large delay are studied. Critical cases in the problem of the stability of the zero equilibrium state are singled out, and it is shown that all of them have infinite dimensions. Applying special methods of infinite normalization, we construct quasinormal forms, namely, nonlinear boundary value problems of the parabolic type, whose nonlocal dynamics determine the behavior of the solutions of the initial system in a small neighborhood of the equilibrium state. These quasinormal forms contain either two or three spatial variables, which emphasizes the complexity of the dynamical properties of the original problem.

Suggested Citation

  • Sergey Kashchenko, 2024. "Chains with Connections of Diffusion and Advective Types," Mathematics, MDPI, vol. 12(6), pages 1-28, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:790-:d:1353273
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    References listed on IDEAS

    as
    1. Sergey Kashchenko, 2022. "Infinite Turing Bifurcations in Chains of Van der Pol Systems," Mathematics, MDPI, vol. 10(20), pages 1-10, October.
    2. Sergey Kashchenko, 2023. "Asymptotics of Regular and Irregular Solutions in Chains of Coupled van der Pol Equations," Mathematics, MDPI, vol. 11(9), pages 1-34, April.
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