22 March 1996 Chaotic behavior analysis for the neuron's oscillatory models
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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.
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S. N. Charankevich, Halina V. Grushevskaja, 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); doi: 10.1117/12.235954; https://doi.org/10.1117/12.235954
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