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Journal of Applied Nonlinear Dynamics 1(4) (2012) 407--412 | DOI:10.5890/JAND.2012.07.002

T.V. Karamysheva; N.A. Magnitskii

Institute for Systems Analysis of RAS, Prospec 60-let Oktyabrya, Moscow, Russia

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Abstract

In the present work it is shown, that the FitzHugh-Nagumo type system of partial differential equations with fixed parameters can have an infinite number of different stable wave solutions, traveling along the space axis with arbitrary speeds, and also traveling impulses and an infinite number of different states of spatiotemporal (diffusion) chaos.Those solutions are generated by cascades of bifurcations of cycles and singular attractors according to the FSM theory (Feigenbaum-Sharkovskii-Magnitskii) in the threedimensional system of Ordinary Differential Equations (ODEs), to which the FitzHugh-Nagumo type system of equations with self-similar change of variables can be reduced.

Acknowledgments

The research was supported by the Russian Foundation for Basic Research (projects nos. 11-07-00126a and 12-07-00271a) and the program ONIT RAS (projects nso. 1.9, 3.5).

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