ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Nekorkin V. I., Shchapin D. S., Dmitrichev A. S. Complex wave dynamics of ensemble of neuron-like elements with complex threshold excitation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 1, pp. 3-22. DOI: 10.18500/0869-6632-2007-15-1-3-22

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Complex wave dynamics of ensemble of neuron-like elements with complex threshold excitation

Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences
Shchapin D. S., Institute of Applied Physics of the Russian Academy of Sciences
Dmitrichev Aleksej Sergeevich, Institute of Applied Physics of the Russian Academy of Sciences

We present the analysis of spatiotemporal dynamics in the system modeling collective behaviour of ensemble of electrically coupled neuronal cells. The dynamics of local element is described by the FitzHugh – Nagumo system with complex threshold excitation. Heteroclinic orbits and corresponding wave fronts are investigated. We show that in the phase space of system for traveling waves there exist heteroclinic cycle formed by separatrix manifolds of two saddle-foci. It is shown that the existence of such cycle leads to complex spatiotemporal dynamics of ensemble including rhomb-like and nonstationary oscillating wave structures.

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