Global Stability Analysis Of Neural Networks With Time Delays

This paper addresses the stability of the neural networks systems with time-varying delays. By constructing proper Lyapunov functions and using the liner inequality, several sufficient conditions for globally asymptotic stability and globally exponential stability of neural networks with time-varying delays are obtained, and the criterion in this paper have improved and developed the previous known results in some literatures.We generalize the content as following:(i) By using the method of the proper Lyapunov functions and Jacobsthal inequality, we study the globally asymptotic stability and globally exponential stability of bidirectional associative memory neural networks, Hopfield neural networks and competitive neural networks with time delays. Moreover, the sufficient criteria obtained here are computationally more flexible and more efficient than many other existing criteria.(ii) Based on the proper Lyapunov functions and the inequality technical, some sufficient conditions are presented in this paper for global exponential stability of delay competitive neural networks with different time scales. And it is shown that the new results impose weaker conditions for the exponentially stability. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.(iii ) This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall -Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.