The dynamical mechanism of a kind of noise-induced complete chaotic synchronization of two non-coupled periodically driven FitzHugh-Nagumo neuron models and strange non-chaotic attractor

Abstract

The dynamical mechanism of noise-induced complete chaotic synchronization of two uncoupled periodically driven FitzHugh-Nagumo (FHN) neuron models is initially researched in this paper. Here we show: based on a nonlinear dynamical analysis and numerical evidence, that under the perturbation of weak noise strange non-chaotic attractor (SNA) can be induced to appear in FHN neuron model, which is formed through transitions among chaotic attractor, periodic attractor and chaotic saddle in two sides of boundary crisis point of system respectively. When SNA appears the maximum Lyapunov exponent of the attractor is non-positive and there is thus no sensitive dependence on initial conditions. The two FHN neuron models are identical but there is slight difference between their initial states. After the attractors of the two FHN neuron models become strange non-chaotic attractors from strange chaotic attractors under the appropriate noise, the responses of the two systems, which are no sensitive dependence on initial conditions, are complete synchronous. The dynamical mechanism of noise-induced complete chaotic synchronization of two non-coupled FHN neuron models is related to the strange non-chaotic attractor induced to appear by noise.