Dynamic Behavior Analysis Of Two Kinds Of Variable Coefficient Impulsive Delay Recurrent Neural Networks

Recurrent neural networks such as Hopfield neural networks, cellular neural networks and Cohen-Grossberg neural networks, eta, have potential applications in signal and image processing, associative memory, pattern recognition, parallel computation and optimization, and so on. Because the dynamic characteristics of neural networks such as equilibrium point, stability, limit cycle and chaos theory are the prerequisite of their applications, and always occupy an important position in their theoretical research. Time-delays in the delivery process of neural network signals are inevitable, it means that neural networks model should be related to the state in the past time and often leads to instability, and even periodic oscillations or chaos due to its great influence on the dynamic characteristics of the network model. Moreover, abrupt change in the voltage can lead wrong circuit, which is called the typical impulsive phenomenon, it can affects the transient behavior of the neural networks. Thus it is very necessary to consider the impact on both time-delays and impulsive in the study of stability for neural networks.In addition, over the past two decades, the synchronization problem of chaotic systems has been widely investigated due to its potential applications in many differ-ent fields including secret communication, chemistry, biology, information science, optics and so on. In fact, chaotic synchronization is the key to achieve secret com-munication, and chaotic secret communication become a new and efficient secret way since it has real-time and high secrecy. Therefore it has important value in practice to investigate the system’s synchronization problem.Based on the above considerations, we intensively analysis the dynamic be-haviours of two classes of recurrent neural networks with time-delays in this thesis. The main work is as follows:1. We study the stability of periodic solution for a class of recurrent neu-ral networks with time-varying delay and impulsive. By constructing appropriate Lyapunov functional and using the linear matrix inequality approach, a sufficient condition is provided to ensure the global exponential stability of this network. The obtained result improves some existing one, and reduce the system’s conservative. Because the given conditions are expressed by linear matrix inequalities, it is easy to implement using the LMI toolbox of Matlab software. Numerical simulation not only supports the correctness of the obtained result, but also illustrates that the given conditions are easy to check.2. We study the exponential synchronization for a class of variable coefficients recurrent neural networks with time-varying delay and impulsive. Since the connec-tion weights in the system depend on state of the neuron, a sufficient condition is given to ensure the exponential synchronization of this network by using set-valued map and differential inclusion theory, algebraic inequality technique and construct-ing appropriate Lyapunov functional. Numerical example not only supports the correctness of the obtained result, but also illustrates that the given conditions are easy to check.