Stability Of Two Kinds Of Time - Varying Impulsive Delay Neural Networks

Since neural networks have wide applications in many fields include pattern recognition, associative memory, signal processing, graphical optimization and so on, its dynamic nature, especially for stability, becomes a research focus in the field of neural networks. Due to the limited switch speed of the amplifier, the influence of time delays is inevitable. Thus the study of neural networks with time delays is very important. In addition, many systems may suffer suddenly to be disturbed in a very short time when the systems are in the process of continuous gradual, then their original trajectory is changed and the impulsive phenomena is occurs. This phenomena can affect the transient behavior of the networks, therefore the introduction of pulse disturbance in the neural networks will further expand its application scope. In general, the dynamic system includes unstable and stable impulsive sequence. Unstable impulsive sequence inhibits the stability of dynamic system, and the stability of the impulsive sequence improves the stability of the dynamic system. The neural networks are controlled by the dynamic system, so it is very necessary to consider the influence of impulsive disturbance and these two kinds of impulsive sequence simultaneously in the study of neural networks. This thesis will study the dynamic behavior of neural networks with the influence of time delays and variable impulsive.In chapter1, we first review the development and research status of the neural networks, analyze the influence of variable pulse and time delays to neural networks, and introduce the research progress of neural networks with variable impulsive and time delays in recent years, and the development of neural networks with interval weighed matrix. Next, we give preliminary knowledge of this thesis, which includes some definitions, theorems and inequalities, and then introduce the theories of the stability, give the neural-network models with time-varying impulsive delays. Fi-nally, we illustrate the main works in this thesis.Chapter2studies the global exponential stability for the Hopfield neural net-works with time-varying impulse. By constructing a proper Lyapunov function and applying the comparative method, we get the sufficient conditions of global expo-nential stability for the model with the time-varying impulse. Numerical examples are proved to illustrate the validity of the results. In chapter3, for a class of interval matrix, we study the global exponential stability of neural networks with time-varying impulse and time delays. By using upper and lower bounds of the interval matrix and comparative method, we give a sufficient condition of the global exponential stability for neural networks model with variable parameters, time-varying impulse and delay. The obtained results extends the results of existing literature. Numerical examples are proved to illustrate the usefulness of the results.