Exponential and adaptive lag synchronization of inertial Cohen–Grossberg neural networks with unbounded distributed delays

Abstract

The primary focus of this article is to address the challenge of achieving exponential and adaptive chaotic lag synchronization in inertial Cohen-Grossberg neural networks (ICGNNs). This problem is investigated in the context of discrete, unbounded distributed delays. Importantly, the approach taken here directly constructs a Lyapunov functional, bypassing the need for a standard reduced-order transformation typically employed for inertial neural networks (INNs). In the initial stages, a feedback control scheme is formulated, accompanied by the introduction of a non-trivial Lyapunov functional. This function incorporates state variables and their derivatives, serving as a key tool in analyzing exponential lag synchronization. Multiple criteria involving various parameters are deduced. Additionally, an adaptive control strategy is developed. This strategy facilitates the adjustment of control gains, ensuring asymptotic lag synchronization. The method of undetermined coefficients is applied to construct the Lyapunov functional, and the Barbalet Lemma is utilized to support the achievement of asymptotic lag synchronization. The article concludes with specific parameter settings for numerical validation. Illustrative numerical examples are presented to effectively showcase the practical validity of the theoretical findings. This example serves to substantiate the proposed model and the efficacy of the derived theoretical results.