Exponential stability analysis of Cohen-Grossberg neural networks with time-varying delays

Abstract

In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks with Time Delays under Dirichlet Zero Boundary Value

“…where the positive number δ is small enough, and so is δ 1 . And then 46) which together with inf H J 0 implies that all u ∈ E(µ 1 ) with ∥u∥ H δ are the stationary solutions of the reaction diffusion system (3.38). Moreover, E(µ 1 ) implies that there are infinitely many positive stationary solutions and infinitely many negative stationary solutions for the reaction diffusion system (3.38).…”

“…where a = 0.002π 2 + 3.575, b = 0.005, satisfying a > b > 0. By employing [46,Lemma 3] or the methods in the proof of [40,Theorem 3], we can derive that the zero solution of the system (3.43) is globally exponentially stable with the convergence rate 1 2 , where λ > 0 is the unique solution of the equation λ = a − be λτ . That is, the constant equilibrium point u * of the reaction diffusion system (3.33) is globally exponentially stable, and so u * is the unique equilibrium point of the reaction-diffusion system.…”

Global exponential stability and existence of anti-periodic solutions to impulsive Cohen-Grossberg neural networks on time scales

“…In recent years, the dynamical behaviors of Cohen-Grossberg neural networks with delays have been studied by many researchers (see e.g. [9], [17]- [19], [21], [25]).…”