Exponential Stability of Stochastic Inertial Cohen–Grossberg Neural Networks

Abstract

In this paper, we adopt two methods to study the problem. Initially, directly from the second-order differential equation, we obtain a sufficient condition (SC) for the mean square exponential stability (MSES) of the system at the equilibrium point by constructing a suitable function and applying some properties of calculus. Thereafter, the system is transformed into a vector form, using the basic solution matrix of linear differential equation, constructing a piecewise function and using the generalized Halanay one-dimensional delay differential inequality, another SC is given for the P-moment exponential stability (PMES) of the system at the equilibrium point. Finally, two examples are used to investigate the correctness and demonstrate that each SC has own advantage, the suitable theorem can be selected according to the parameters.