Pulse Variable Time Delay Dynamic Behavior Of The Static Neural Network

In recent years, neural networks have been widely applied in many areas, in-cluding associative memory, pattern recognition, signal processing, combinatorial optimization, image processing, intelligent controlled and so on. According to the choice of the basic variables of system, neural networks can be classified as local neural networks(the internal states of neurons)or static neural networks(the exter-nal states of neurons). Local neural network have applied in many areas including optimization calculation and associative memory. Static neural network has more advantages in solving the variation inequalities and optimization problems. In prac-tice, neural network is often influenced by delay and impulse. On the one hand, due to finite switching speeds of the neuron amplifiers, time delays are unavoidable, which can result in instability or oscillation. On the other hand, the faulty circuit produced by the abrupt changes in the voltages. It is typical impulse phenomena, which can affect the transient behavior of the neural network. Thus, it is neces-sary to consider both impulsive and delay effect on the stability of a neural network model. Therefore in this paper, investigates the dynamic behavior of static neural networks with impulsive effect and time-varying delays.In chapter 1, we first review the history and basic properties of neural networks, and analyze delay and impulsive influence on the stabilities of neural networks. Then some methods and progresses of the neural networks with time-delay and impulse are introduced. Finally,we summarize the main work of this paper.Chapter 2. provides preliminaries, which include some definitions, lemmas, in-equalities and some stability theories. Then we introduce the static neural network model with time-varying delays and impulses.In chapter 3, we study the asymptotic stability of static neural networks with time-varying delays and impulses. By defining Lyapunov functional and using linear matrix inequality, the delay dependent stability of the system is proved. The effect of delay and impulse are simultaneously considered, the obtained result are more general and applied a broad class problems. Finally, the effectiveness and feasibility of obtained theoretical results are illustrated by two examples.In chapter 4.we further investigate the global exponential stability of static neu-ral networks with time-varying delays and impulses. By constructing two Lyapunov functionals, and using linear matrix inequality methods, two sufficient conditions are provided to ensure the delay dependent stability. Compared with the existing results, the given stability conditions are less conservativeness, easy to checked and applied to a broad class problems. Finally, the obtained results are supported by two simulations results.