Convergence of asymptotic systems in Cohen-Grossberg neural network models with unbounded delays

Abstract

In this paper, we investigate the convergence of asymptotic systems in non-autonomous Cohen--Grossberg neural network models, which include both infinite discrete time-varying and distributed delays. We derive stability results under conditions where the non-delay terms asymptotically dominate the delay terms. Several examples and a numerical simulation are provided to illustrate the significance and novelty of the main result.

Figures (2)

• Figure 1: Numerical simulation of three solutions $(x_1(t),x_2(t))$ of system \ref{['non-periodic ex']}, with initial condition $\varphi(s)=(-\mathrm{e}^s/2,\cos(s)/2)$, $\varphi(s)=(\cos(s)/2,-\mathrm{e}^s/2)$, $\varphi(s)=(\sin(s),\mathrm{e}^s-1)$ for $s\leq0$, respectively, at $t_0=0$.
• Figure 2: Numerical simulation of three solutions $(x_1(t),x_2(t))$ of system \ref{['non-periodic ex']}, with initial condition $\varphi(s)=(-\mathrm{e}^s/2,\cos(s)/2)$, $\varphi(s)=(\cos(s)/2,-\mathrm{e}^s/2)$, $\varphi(s)=(\sin(s),\mathrm{e}^s-1)$ for $s\leq0$, respectively, at $t_0=0$.

Theorems & Definitions (21)

• Remark 2.1
• Definition 2.1
• Lemma 3.1
• proof
• Lemma 3.2
• proof
• Theorem 3.3
• proof
• Corollary 3.4
• Corollary 4.1