Abstract

A complex network is a complex set composed of several elementary units which have certain characteristics and functions and interact with each other. In recent years, the complex network has become one of the research hotspots of nonlinear science. Many scholars in the fields of control, mathematics, computer, biology and economy have devoted themselves to the research of complex networks. This study focuses on the stability of pinning impulse synchronization for the directed complex dynamic networks. From the Impulse Control Theory, a simple and general synchronization criterion for complex dynamic networks is obtained. Furthermore, the obtained results are applied to a small-world network consisting of a convolution neural network (CNN) and a Hodgkin-Huxley model neuron oscillator as power nodes. The numerical simulation shows the correctness of the obtained theoretical results and the validity of the control method.

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