Globally attractive periodic solutions of continuous-time neural networks and their discrete-time counterparts

Authors:
Changyin Sun;Liangzhen Xia;Chunbo Feng
Affiliations:
College of Electrical Engineering, Hohai University, Nanjing, China;Research Institute of Automation, Southeast University, Nanjing, China;Research Institute of Automation, Southeast University, Nanjing, China
Venue:
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Year:
2005

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Abstract

In this paper, discrete-time analogues of continuous-time neural networks with continuously distributed delays and periodic inputs are investigated without assuming Lipschitz conditions on the activation functions. The discrete-time analogues are considered to be numerical discretizations of the continuous-time networks and we study their dynamical characteristics. By employing Halanay-type inequality, we obtain easily verifiable sufficient conditions ensuring that every solutions of the discrete-time analogue converge exponentially to the unique periodic solutions. It is shown that the discrete-time analogues inherit the periodicity of the continuous-time networks. The results obtained can be regarded as a generalization to the discontinuous case of previous results established for delayed neural networks possessing smooth neuron activation.