Stability And Synchronization Control Of Several Kinds Of Impulse Neural Network Systems

Neural networks are mathematical models in order to simulate the neuronal network of the human brain,and are now extensively applied to pattern recognition,image pro-cessing,parallel computing,associative memory optimisation and many other fields.The existence of impulsive effects frequently greatly affects the performance of the system.On the other hand,in neural network systems,synaptic transmission can be seen as a noisy process accompanied by neurotransmitter release and other random factors,and dy-namical analysis and synchronization control of impulsive stochastic neural networks has become an important research topic recently.This paper combines Lyapunov stability theory,the comparison principle,matrix decomposition theroy,the generalized impul-sive Halanay differential inequality and the general average impulsive interval approach to investigate the issues of stability and synchronization control for several special types of impulsive stochastic neural network systems.The first chapter mainly introduces the research background,significance,research status,main research content and innovation points of the impulsive stochastic neural network system.Chapter 2 investigates the input-to-state stability problem of a stochastic mixed time-delay neural network system with hybrid impulsives.Both stable and unstable impulses are introduced simultaniously into the model,and the effect of the hybrid impulses on the system performance is considered.Concretely,for the stochastic neural network system with hybrid impulsives and mixed delays,the relevant criteria for input-to-state stability are derived when the system contains external inputs.Sufficient conditions for the ex-ponential stability of the mean-square moment of the neural networks are obtained when the system input is zero,and finally the validity of the theoretical results is verified by numerical simulations.Chapter 3 discusses the issue of pth moment exponential synchronization for stochas-tic impulsive neural network systems with time-varying coefficients and unbounded de-lays.Firstly,an impulsive generation assumption is proposed which cover more exten-sive impulse sequences.Meanwhile,a more general time-varying impulsive differential inequality is established for a class of stochastic impulsive neural networks.Secondly,the time-delay term is relaxed by introducing a monotonically increasing non-negative func-tion,which leads to the more general result.Subsequently,by designing time-varying feedback controllers,the pth moment synchronization is achieved under several given sufficient conditions.Finally,numerical simulations verify the feasibility of our theoret-ical results.Chapter 4 considers the synchronization problem of stochastic coupled inertial neural networks with hybrid impulsives.For the neural network system with inertial terms,cou-pling terms,stochastic disturbances and impulsive effects,when the average impulsive interval is bounded constant,one criterion for consistent synchronization in mean-square moment is obtained by utilizing the stochastic stability theory and matrix decomposition approach.When the average impulse interval convergenes to the infinity,accordingly,the sufficient conditions of consistent synchronization is acquired.Finally,the validity of the theoretical results is verified by numerical simulations.Chapter 5 concludes the above investigation and points out the directions for future improvement and further research.