Asymptotic Behavior Of Some Dynamical Systems With Delays And Applications

This paper is concerned with global asymptotic behavior of some dynamical sys-tems which are described by differential equations with delays and their applications.In Chapter 1, we introduce the development history of asymptotic behavior ofdynamical systems. Some important directions and interesting results will be shown toreaders.In Chapter 2, we discuss the dissipativity of a class of differential inequalitiesintroducing by Dini derivative. Combining with the measure of nonlinear operator, weresearch the dissipativity of differential equations with delay and give some sufficientconditions for the uniformly dissipativity of Hopfield neural networks with delay.In chapter 3, we study dissipativity and global attracting set of a general classof neural networks models with continuously distributed delays by using nonnegativematrix and differential inequality technique. Some new results are derived under moregeneral conditions.In Chapter 4, we consider p-moments ultimate boundedness and global attractingset of stochastic differential equations with discrete delays. By using nonnegative ma-trix and Ito formula, and combining with the characteristic of stochastic process, weget some new criterions and related results.