Stability of a non-autonomous reaction-diffusion food chain system with feedback control and time-varying delays
摘要
This study develops a novel non-autonomous diffusion-driven food chain model incorporating time-varying delays, feedback control mechanisms, and a Michaelis-Menten functional response to address limitations in traditional ecological models. By integrating spatiotemporal dynamics with realistic biological interactions, we derive rigorous theoretical conditions for the existence and global asymptotic stability of spatially homogeneous periodic solutions using a hybrid analytical framework combining fixed point theory, Lyapunov functionals, and limit approximation methods. The model accounts for environmental fluctuations and delayed responses, revealing critical dependencies of population persistence on diffusion rates, feedback control strengths, and delay structures. Numerical simulations parameterized with empirical data validate these findings, demonstrating delay-induced oscillations, trophic cascade propagation, and feedback-mediated stabilization under environmental stochasticity. Results highlight the model’s capacity to predict population resilience in changing environments, offering mechanistic insights for conservation biology, pest management, and ecosystem resilience assessment. This work bridges a gap between theoretical reaction-diffusion systems and complex ecological realities, providing a foundational framework for predicting species responses to climate change and habitat fragmentation while emphasizing the stabilizing role of adaptive feedback in maintaining ecosystem balance.