Global exponential stability in Lagrange sense of continuous-time recurrent neural networks

Abstract

In this paper, global exponential stability in Lagrange sense is further studied for continuous recurrent neural network with three different activation functions. According to the parameters of the system itself, detailed estimation of global exponential attractive set, and positive invariant set is presented without any hypothesis on existence. It is also verified that outside the global exponential attracting set; i.e., within the global attraction domain, there is no equilibrium point, periodic solution, almost periodic solution, and chaos attractor of the neural network. These theoretical analysis narrowed the search field of optimization computation and associative memories, provided convenience for application. © Springer-Verlag Berlin Heidelberg 2006.