Global boundedness and asymptotic stability for a cognitive consumer-resource system with memory-driven taxis

Abstract This paper investigates a cognitive consumer-resource model incorporating memory-dependent perception dynamics, modeled through a reaction-diffusion-advection system. We rigorously demonstrate the global existence and boundedness of classical solutions in spatial dimensions n ≤ 3 for arbitrary parameter values. For n > 3, solutions remain globally bounded under sufficiently small values of the perceptual sensitivity parameter χ . By employing Lyapunov functionals and parabolic regularity theory, we prove the global asymptotic stability of two equilibria: the constant coexistence steady state and the consumer-free constant steady state. For the constant coexistence steady state, solutions demonstrate exponential convergence under spectral gap constraints, whereas the consumer-free constant steady state exhibits algebraic decay. The analysis highlights how memory-driven taxis, mediated by χ , critically regulate system dynamics. This work bridges cognitive mechanisms and ecological models, providing explicit quantitative thresholds for stability in spatially structured environments.