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Title: Lyapunov analysis of the spatially discrete-continuous system dynamics
Authors: Maximenko, V.A.
Hramov, Alexander E.
Koronovskii, Alexey A.
Makarov, V.V.
Postnov, Dmitry E.
Balanov, Alexander G.
Keywords: Lyapunov exponents
Dynamical chaos
Spatially extended system
System with the small number of degrees of freedom
Numerical simulation
Reaction-diffusion model
Spreading depression
Issue Date: 2017
Publisher: © Elsevier
Citation: MAXIMENKO, V.A. ... et al, 2017. Lyapunov analysis of the spatially discrete-continuous system dynamics. Chaos, Solitons and Fractals, 104, pp. 228-237.
Abstract: 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.
Description: 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
Sponsor: This work has been supported by Russian Science Foundation (grant 14-12-00224).
Version: Accepted for publication
DOI: 10.1016/j.chaos.2017.08.021
URI: https://dspace.lboro.ac.uk/2134/26412
Publisher Link: https://doi.org/10.1016/j.chaos.2017.08.021
ISSN: 0960-0779
Appears in Collections:Published Articles (Physics)

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