Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.2, pp.11--24

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 2, pp.11--24

Chaos in Near-Hamiltonian Systems with Singular Perturbation: Applications to Oscillatory Model of Hodgkin--Huxley Neuron.
H.V. Grushevskaya

Neuron's oscillatory model is transformed to the form of near-Hamiltonian system with singular coefficients. We demonstrate that singular coefficients can be considered as a perturbation of the system by virtue of discrete sequence of kicks. The linearization of the perturbation in the vicinity of periodical solution for a given kick allows us to rewrite the system as a matrix Schrödinger equation for two-level quantum system in a resonant quasi-monochromatic field. As a result, the original system demonstrates chaotic behavior through the cascade of period doubling bifurcations. The bifurcations in this case correspond to the series of quantum nutation of nutations.

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