Stability Analysis For A Class Of Discrete Neural Networks With Discontinuous Activation Functions

In this thesis,we consider the stability for the following discrete neural network systems with discontinuous activation functions(?).The stability involves the boundedness,nonoscillation and asymptotic behaviors.The content includes four chapters and the outline for each chapter is listed as follows:The first chapter states the research background and origin of this project.To begin with,we briefly review the history and development of neural networks via several representative mathematical models.Then,we recall the current status of researches on the discontinuous neural networks.Finally,we introduce our motivation to consider the research topics of this thesis.The second chapter is the preliminaries of this thesis.First,the notations and formulations of considered discrete neural networks are given.Then,some basic concepts are listed and two lemmas are also shown.The first lemma will be used to consider the exponential asymptocity,and the second will guarantee the existence of equilibrium solutions of(?)for the constant inputs.The third chapter is devoted to investigate the boundedness and nonoscillation of the system(?).For the boundedness,with the method of mathematical analysis,we obtain three sufficient criteria for system(?)being bounded.For the nonoscillation,we divide it into two parts.For the first,two criteria ensuring the eventually constant sign of the solutions of system(?)are offered.For the second,sufficient conditions for the global constant sign and final constant sign between the solutions of system(?)and the equilibrium solution of(?)with constant inputs are obtained,respectively.The fourth chapter discusses the asymptotic behaviors of the system(?)in two parts.In the first part,by constructing suitable Lyapunov functions,two criteria are obtained for the system(?)asymptotically nearing to the equilibrium solution of(?)with constant inputs;In the second part,under the premise that the activation functions are bounded,a sufficient criterion is given,which guarantees the asymptotic behaviors of the solutions of system(?).Then,a sufficient condition is attained,which guarantees the solutions of system(?)exponentially asymptotically nearing to the equilibrium solution of(?)with constant inputs.Under the premise that the activation functions are not required to be bounded,a sufficient criterion with a well-defined convergence index is attained,which guarantees system(?)being exponentially asymptotically the equilibrium solution of its corresponding constant input system.In the discussions in chapter 3 and chapter 4,we provide several appropriate examples to verify the feasibility of our main results.The work of this thesis partly fills the gap as well as extends the results^[34].