Positive invariant and global exponential attractive sets of neural networks with time-varying delays

Authors:
Xiaoxin Liao;Qi Luo;Zhigang Zeng
Affiliations:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China;Department of Information and Communication, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China;School of Automation, Wuhan University of Technology, Wuhan, Hubei 430070, China
Venue:
Neurocomputing
Year:
2008

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Abstract

In this paper, global exponential stability in Lagrange sense is further studied for various continuous-time delayed recurrent neural network with two different types of activation functions. Based on the parameters of the systems, detailed estimation of global exponential attractive sets and positive invariant sets are presented without any hypothesis on the existence. It is also verified that outside the global exponential attracting set; i.e., within the global attraction domain, there is no equilibrium state, periodic state, almost periodic state, and chaos attractor of the neural network. These theoretical analysis narrows the search field of optimization computation, associative memories, chaos control and synchronization and provide convenience for applications.