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.
Highlights
In recent years, the pinning control and synchronization of complex dynamic networks have attracted wide attention from various fields, such as science and engineering technology [1,2]
In the literature [5], based on the observation of the state of all the nodes in the network, the overall synchronization convergence criterion of the complex dynamic network is obtained by using the impulse control method
The obtained results are applied to a small-world network composed of convolution neural network (CNN) and Hodgkin-Huxley neuron oscillators as power nodes
Summary
The pinning control and synchronization of complex dynamic networks have attracted wide attention from various fields, such as science and engineering technology [1,2]. There are many important results for pinning impulse control of complex dynamic networks with different types and topologies [3,4,5,6,7,8]. In the literature [4, 7], a new analysis method has been proposed on the stability of pinning impulse of complex (time-lag) dynamic networks. Some simple and general robust synchronization criteria for complex (time-lag) dynamic networks are obtained based on local linearization technology. In the literature [5], based on the observation of the state of all the nodes in the network, the overall synchronization convergence criterion of the complex dynamic network is obtained by using the impulse control method. In the Introduction section, present clearly and briefly the problem investigated, with relevant references
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