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Lyapunov analysis of the spatially discrete-continuous system dynamics

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journal contribution
posted on 2017-09-07, 12:54 authored by V.A. Maximenko, Alexander E. Hramov, Alexey A. Koronovskii, V.V. Makarov, Dmitry E. Postnov, Alexander BalanovAlexander Balanov
The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

Funding

This work has been supported by Russian Science Foundation (grant 14-12-00224).

History

School

  • Science

Department

  • Physics

Published in

Chaos, Solitons and Fractals

Volume

104

Pages

228 - 237

Citation

MAXIMENKO, V.A. ... et al, 2017. Lyapunov analysis of the spatially discrete-continuous system dynamics. Chaos, Solitons and Fractals, 104, pp. 228-237.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2017

Notes

This paper was accepted for publication in the journal Chaos, Solitons and Fractals and the definitive published version is available at https://doi.org/10.1016/j.chaos.2017.08.021

ISSN

0960-0779

Language

  • en