Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 24, Issue 11, Pages 1749-1762Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2013.2262638
Keywords
Attractive set; equilibrium point; multistability; time-varying delays
Categories
Funding
- Australian Research Council
- Natural Science Foundation of China [60974021, 61125303]
- National Basic Research Program of China 973 Program [2011CB710606]
- F. Y. Tung Education Foundation [111068]
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In this paper, we investigate multistability of two kinds of recurrent neural networks with time-varying delays and activation functions symmetrical about the origin on the phase plane. One kind of activation function is with zero slope at the origin on the phase plane, while the other is with nonzero slope at the origin on the phase plane. We derive sufficient conditions under which these two kinds of n-dimensional recurrent neural networks are guaranteed to have (2m + 1)(n) equilibrium points, with (m + 1)(n) of them being locally exponentially stable. These new conditions improve and extend the existing multistability results for recurrent neural networks. Finally, the validity and performance of the theoretical results are demonstrated through two numerical examples.
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