Chaotic behavior analysis for the neuron's oscillatory models

S. N. Charankevich; Halina V. Grushevskaja; George G. Krylov

doi:10.1117/12.235954

22 March 1996 Chaotic behavior analysis for the neuron's oscillatory models

S. N. Charankevich, Halina V. Grushevskaja, George G. Krylov

Proceedings Volume 2760, Applications and Science of Artificial Neural Networks II; (1996) https://doi.org/10.1117/12.235954
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

A oscillatory model of a Hodgkin and Huxley's neuron was proposed. It was shown that the unfolding degeneracy of this system in the vicinity of homoclinic trajectory go to a cascade of period-doubling bifurcations with the subsequent transition in deterministic chaos. A method of finding of homoclinic points in a system of ODE, based on the consideration of a system of partial differential equations of lower dimension in WKB-approximation is proposed.

Citation Download Citation

S. N. Charankevich, Halina V. Grushevskaja, and George G. Krylov "Chaotic behavior analysis for the neuron's oscillatory models", Proc. SPIE 2760, Applications and Science of Artificial Neural Networks II, (22 March 1996); https://doi.org/10.1117/12.235954

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