The Exponential Stability Analysis Of Periodic Solution For Some Classes Of Impulsive Neural Networks

In1983, Cohen-Grossberg neural network (CGNN) was initially presented by Cohen and Grossberg (See the literature [1]), which includes the famous Hopfield neural net-works (HNNs), cellular neural networks (CNNs) and Lotka-Volterra competition models (LVCMs) as its special cases. Recent years, CGNNs Neural network has been rapid devel-opment, has been widely applied in many fields of science, such as optimization, pattern recognition, associative memory, robotics and computer vision.Many evolution processes exhibit abrupt changes of their states at certain moments, This creates the impulse. Stability is one of the major problems encountered in design and applications of neural networks, periodic oscillation is an important dynamical behavior for non-autonomous neural networks. The properties of periodic oscillatory solutions represented various storage patterns or memory patterns, There are many applications in scientific research.There are five sections in all. The first section is introduction:First, this section describes the history, the background of neural networks; Secondly, it introduces the development of pulse neural networks, the actual significance of the research status and research results; Finally, the research content of this paper is an overview and chapters.The Section2is preliminaries:Introduces some common definitions and some relevant Theorems of stability.The Section3studies the exponential stability of a class of impulse with time de-lay cellular neural networks. Particularly, we base on p-norm and oo-norm by Young inequality, Lyapunov functional method and analysis method, Get the system is expo-nential stability. Finally, two example with numerical simulations is given to illustrate our results.The Section4discusses the existence and stability of periodic solutions for Cohen- Grossberg neural networks with impulsive effects. By using a impulsive differential in-equality and Banach fixed point theorem, some analysis techniques and by constructing Lyapunov functions, we obtain some new sufficient conditions for the existence and ex-ponential stability of the periodic solutions of Cohen-Grossberg neural networks. Finally, One example is presented to illustrate the effectiveness of proposed method.The Section5studies the existence and exponential stability of anti-periodic solutions for Cohen-Grossberg neural networks with impulsive effects. We obtain the existence and exponential stability of the system anti-periodic solutions. Finally, a numerical example is given to show the effectiveness of the proposed synchronization method.