Synchronization Analysis And Control Of Complex-valued Neural Networks With Hybrid Impulses

In recent years,many valuable results on the synchronization of neural networks have been obtained.However,it is worth pointing out that these studies are mainly based on the traditional real-valued neural networks(RVNNs)model.Complex-valued neural networks(CVNNs)are more general and complicated than real-valued neural networks.In this paper,the master-slave synchronization of complex-valued neural networks is studied by using hybrid impulsive control method,Lyapunov functional method,average impulse interval(AII)and average impulse gain(AIG).This thesis is divided into four chapters and the main contents are as follows:In the first chapter,the current research status of synchronization of complex-valued neural networks and some theories and existing results of impulsive control methods are summarized.The main contents and contributions of this paper are expounded according to the above-mentioned analysis.In the second chapter,exponential synchronization for master–slave time-varying delayed complex-valued neural networks is investigated under hybrid impulsive controllers.Hybrid impulsive controllers is the extension of impulsive controllers,which can simultaneously permit synchronizing as well as desynchronizing impulses in one impulsive sequence,i.e.,hybrid impulses.We separate complex-valued neural networks into their real and imaginary parts,which leads to two real-valued neural networks.Based on the concepts of average impulsive interval and average impulsive gain,we find that master–slave exponential synchronization for the real and imaginary parts of complex-valued neural networks can be realized via hybrid impulsive control under certain conditions.By employingthe Lyapunov method,sufficient criteria are established to guarantee synchronization of the given master–slave complex-valued neural networks.Finally,the validity of the obtained results is demonstrated via a numerical example.In the third chapter,the problem of master-slave exponential synchronization is studied when the activation functions of complex-valued neural networks cannot be separated into real and imaginary parts.Based on the concepts of average pulse interval and average pulse gain,sufficient criteria are given for master-slave synchronization of complex-valued neural networks by using Lyapunov functional method and linear matrix inequality method.Finally,a numerical example is given to verify the validity of the results.In the last chapter,the research work of this paper is summarized and the prospect for the future work is made.