Impulsive Pinning Control in Complex Dynamical Networks with Random Noises and Applications to Firing Neuronal Synchronization

Abstract

In this brief, the problem of impulsive pinning synchronization in complex networks composed of coupled oscillator systems with stochastic noise is investigated. By exploiting the analysis procedure of pinning impulsive stability for undirected coupled dynamical networks developed previously, a simple yet generic criteria of impulsive pinning synchronization in the sense of mean-square for such coupled oscillator network is then presented. Moreover, the results are applied to a small-world (SW) neuronal network comprised of the Hindmarsh–Rose oscillators. It turns out that the firing activities of a single neuron can induce synchronization of the underlying neuronal networks with stochastic noise, which plays a significant role in neural signal encoding and transduction of information processing for neuronal activity. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.