Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function

Authors:
Zhigang Zeng;Tingwen Huang;Wei Xing Zheng
Affiliations:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China and Image Processing and Intelligent Control Key Laboratory of Education Ministry ...;Texas A&M University at Qatar, Doha, Qatar;School of Computing and Mathematics, University of Western Sydney, Sydney, NSW, Australia
Venue:
IEEE Transactions on Neural Networks
Year:
2010

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Abstract

In this brief, stability of multiple equilibria of recurrent neural networks with time-varying delays and the piecewise linear activation function is studied. A sufficient condition is obtained to ensure that n-neuron recurrent neural networks can have (4k - 1)n equilibrium points and (2k)n of them are locally exponentially stable. This condition improves and extends the existing stability results in the literature. Simulation results are also discussed in one illustrative example.