Stochastic asymptotic stability for stochastic inertial Cohen-Grossberg neural networks with time-varying delay

Article type: Research Article

Authors: Xu, Danning | Liu, Wei^*

Affiliations: Yuanpei College, Shaoxing University, Shaoxing, Zhejiang, China

Correspondence: [*] Corresponding author: Wei Liu, Yuanpei College, Shaoxing University, Shaoxing, Zhejiang 312000, China. E-mail: [email protected].

Abstract: This paper studies stochastic asymptotic stability for stochastic inertial Cohen-Grossberg neural networks with time-varying delay. Firstly, the second-order differential equation is converted into the first-order differential equation by appropriate variable substitution. Secondly, the existence of the equilibrium point is derived by using homeomorphic mapping, finite increment formula of Lagrange mean value theorem and linear matrix inequality. The sufficient conditions for the stochastic asymptotic stability of the equilibrium point of the system are derived by defining the appropriate operator, and constructing the appropriate positive Lyapunov function and positive-definite matrix. Thirdly, a numerical example illustrates the correctness of these theorems.

Keywords: Stochastic inertial Cohen-Grossberg neural networks, Time-varying delay, Homeomorphic mapping, Linear matrix inequality, Stochastic asymptotic stability

DOI: 10.3233/JCM-226480

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 23, no. 2, pp. 921-931, 2023