Stability Analysis of Fraction-Order Hopfield Neuron Network and Noise-Induced Coherence Resonance

In this paper, dynamical behaviors of fraction-order Hopfield neuron network are investigated. Firstly, Mittag-Leffler stability analysis is carried out and some sufficient conditions are obtained. On the basis of theoretical analysis, two criteria for determining the stability of fraction-order Hopfield neuron network are presented and comparison between them is given by theoretical analysis along with numerical simulation. According to the proposed criteria, by selecting suitable system parameters, it can be obtained that fraction-order Hopfield neuron network can stabilize to the equilibrium point or an attractor, which can be a periodic orbit or two points. Secondly, considering the inevitable noise in the complex environment of neuron network, the effect of noise on the dynamics of fraction-order Hopfield neuron network is discussed via calculating coefficient of variation and numerical simulations. Results suggest that random noise can cause coherence resonance in fraction-order Hopfield neuron network for certain noise intensity.