Abstract
Origin of the multirhythmicity describing bursting states of real neurons has been explained based on the dynamical behaviour of the proposed oscillatory model of HodgkinHuxley (HH) neuron. The linearization of perturbation in the vicinity of periodical solution for a given kick allows to rewrite the system as a matrix Schrodinger equation for a two-level quantum system in a resonant quasi-monochromatic field. As a result, the original system demonstrates chaotic behaviour through the cascade of period doubling bifurcations. Bifurcations in this case correspond to the series of quantum nutation of nutations. The geometry of the oscillatory neural network phase space is examined and scale-invariant symplectic form and corresponding Hamiltonian are found in neighborhood of quasistable point. A learning rule for the neural networks under consideration to be used for pattern recognition is proposed.
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