Neural Network Synchronization With Impulsive And Infinite Distributed Delay

Neural networks have been widely used in many fields of modern science and technology, such as signal processing, knowledge processing, sensing information processing, automatic control, transportation and communication, neuroscience, electronics, market analysis, entertain-ment, information analysis, retail, aerospace and military fields, etc. Most of the neural network are simulated neurons as the basic unit, and the time pattern of impulse sequence which is extended by the neurons plays a vital role. Impulsive and delay phenomenon of practical problems can be fully considering the instantaneous mutation and the influence of time delay on the state of the system, can be more accurate, more profoundly reflect the transformation law of things. So studing the model of neurons with impulse and delay has been received extensive attention from the researchers.In this paper, we mainly study the asymptotic stability of the neural networks dynamic system with impulse and delay, and the synchronicity of coupled neural network dynamic system. We will combine Lyapunov function with the discrete Halanay-type inequality with distributed delays, use analysis techniques to derive some sufficient conditions which guarantee-ing the asymptotically stable and synchronization of the system, a numerical example is used to illustrate the effectiveness of the proposed method.This paper consists of three parts. The first part begins with a brief introduction to the related background and significance for the research on delayed networks and impulsive systems, then we introduce the progress of the research about the dynamic behavior of the delayed networks and impulsive systems, finally expound the main work in this paper. The second part, we first introduce the neural network models to be investigated, give the simple form of the discrete Halanay-type inequality with distributed delays. Then we derive the conditions making the system asymptotic stability by constructing Lyapunov-Krasovskii function, using some analysis techniques and the given Halanay-type inequality. Finally a numerical example is used to demonstrate our proposed method is effective. The third part, Set up the mathematical model of a class of pulse coupled neural networks with infinite distributed delays. The global synchronization problem of the model is analyzed, some sufficient criteria which guarantee the network synchronization are obtained by constructing proper Lyapunov function and using some inequality analysis. Finally, a numerical example is used to test the feasibility of our method.