Stability analysis of fractional-order impulsive Cohen-Grossberg neural networks with interdisciplinary applications in neurobiology and chemical kinetics

Abstract

This study investigates the global exponential stability of fractional-order Cohen-Grossberg neural networks (CGNN) with impulsive effects. Fractional-order models, which naturally capture memory and hereditary effects, are increasingly used to describe complex biological and chemical processes such as enzyme kinetics, pharmacokinetics, tumor growth, and neural signal transmission. By employing the Caputo fractional derivative and a Lyapunov-Razumikhin functional framework, we derive novel and easily verifiable sufficient conditions that guarantee global exponential convergence of system trajectories toward a unique equilibrium. The proposed results generalize classical integer-order stability criteria to the fractional domain and explicitly account for impulsive perturbations through quantitative bounds that explicitly relate the magnitudes of impulsive effects to the fractional order. This relationship clarifies how memory intensity influences the system's recovery dynamics under impulsive perturbations. A rigorous existence and uniqueness are established via the equivalent fractional integral formulation, and numerical simulations based on a predictor-corrector algorithm confirm the theoretical predictions. The developed framework provides valuable insights into the stability mechanisms of neurobiological spiking dynamics and impulsive chemical dosing in pharmacokinetic systems, where memory effects and sudden shocks coexist.