Stability And Synchronization Of Neural Networks With Impulse Effect

In recent years,the synchronization of impulsive complex networks has attracted wide attention.In practical systems,transmission delay is unavoidable due to the limitation of transmission signals.Therefore,it is of great significance to study the synchronization of complex impulsive networks with time delay.In this thesis,stability of delayed neural networks with impulsive effects is studied and the synchronization of switched coupled neural networks with distributed impulsive effects is studied via an impulsive strength dependent approach.The research contents of this paper can be listed as follows:In the first chapter,we introduce the research background of neural networks and complex networks.In the second chapter,it mainly deals with the stability of delayed neural networks with time-varying impulses,in which both stabilizing and destabilizing impulses are considered.By means of the comparison principle,the impulsive strength-dependent approach and the Lyapunov function approach,sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable.Different from existing results on stability of impulsive systems with average impulsive approach,it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states,and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence.The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval and therefore the proposed impulsive strength-dependent average impulsive interval is more applicable than the usual average impulsive interval.In the end,simulation examples are given to show the validity and potential advantages of the developed results.In the third chapter,it mainly investigates the synchronization of delayed impulsive switched coupled neural networks,in which both synchronizing and desynchronizing impulses are taken into account simultaneously in a distributed way.In addition,both cooperative and competitive interactions are considered.In view of the impulsive strength-dependent average impulsive interval(ISDAII)and the Lyapunov function approach,exponential synchronization problem is investigated for the considered coupled impulsive switched neural networks,where,it is assumed that the average impulsive intervals for different impulsive sequences are distinct.Thus,the proposed ISDAII approach is more general and has a wider application than the usual All approach.Finally,the theoretical results are verified via a numerical example.