Asymptotic stability criteria for a two-neuron network with different time delays

In this paper, the asymptotic stability of a two-neuron system with different time delays has been investigated. Some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of Lyapunov functional. For loc...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2003-01, Vol.14 (1), p.222-227
Main Authors: Liao, Xiaofeng, Wong, Kwok-Wo, Wu, Zhongfu
Format: Article
Language:English
Subjects:
Asymptotic stability
Biological neural networks
Chaos
Computer networks
Concurrent computing
Delay effects
Neural networks
Neurons
Signal processing
Stability criteria
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Summary:In this paper, the asymptotic stability of a two-neuron system with different time delays has been investigated. Some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of Lyapunov functional. For local asymptotic stability, some elegant criteria are also obtained by the Nyquist criteria. We find that one of them depends on the length of delays while the other ones do not. In the latter case, the delays are sometimes called harmless delays. The results obtained have leading significance in the study of neural networks composed of a large number of neurons with different time delays.
ISSN:1045-9227
2162-237X
1941-0093
2162-2388
DOI:10.1109/TNN.2002.806623