Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays. (July 2016)

• Record Type: Journal Article
• Authors: Liu, Peng; Zeng, Zhigang; Wang, Jun
• Is Part Of: Neural networks. Volume 79(2016)
• Page Start: 117
• Page End: 127
• Publication Date: 2016-07
• Subjects: Cohen–Grossberg neural networks -- Multistability -- Non-monotonic activation functions -- Time-varying delays; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2016.03.010
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: This paper addresses the multistability for a general class of recurrent neural networks with time-varying delays. Without assuming the linearity or monotonicity of the activation functions, several new sufficient conditions are obtained to ensure the existence of ( 2 K + 1 ) n equilibrium points and the exponential stability of ( K + 1 ) n equilibrium points among them for n -neuron neural networks, where K is a positive integer and determined by the type of activation functions and the parameters of neural network jointly. The obtained results generalize and improve the earlier publications. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of these exponentially stable equilibrium points can be larger than their originally partitioned subsets. Finally, three illustrative numerical examples show the effectiveness of theoretical results.