Coexistence and local stability of multiple equilibrium points for fractional-order state-dependent switched competitive neural networks with time-varying delays. (March 2023)

• Record Type: Journal Article
• Authors: Wu, Zhongwen; Nie, Xiaobing; Cao, Boqiang
• Is Part Of: Neural networks. Volume 160(2023)
• Page Start: 132
• Page End: 147
• Publication Date: 2023-03
• Subjects: Fractional-order competitive neural networks -- Multistability -- State-dependent switching -- Sigmoidal 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.2022.12.013
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which fractional-order derivative and state-dependent switching are involved at the same time. Some novel criteria are established to ensure that such n -neuron neural networks can have 5 m 1 ⋅ 3 m 2 total equilibrium points and 3 m 1 ⋅ 2 m 2 locally stable equilibrium points with m 1 + m 2 = n, based on the fixed-point theorem, the definition of equilibrium point in the sense of Filippov, the theory of fractional-order differential equation and Lyapunov function method. The investigation implies that the competitive neural networks with switching can possess greater storage capacity than the ones without switching. Moreover, the obtained results include the multistability results of both fractional-order switched Hopfield neural networks and integer-order switched Hopfield neural networks as special cases, thus generalizing and improving some existing works. Finally, four numerical examples are presented to substantiate the effectiveness of the theoretical analysis.