Population-Resource Systems with Perception and Decision Delays: Asymmetric Stability Analysis

Fisheries worldwide exhibit puzzling boom-and-bust cycles despite regulatory efforts, raising questions about what drives these oscillations. We investigate whether temporal delays in monitoring and decision-making contribute to system instability. Our model uses delay differential equations to track an exploiting population and its renewable resources, incorporating two distinct delays: one for perceiving resource status (τ2) and another for implementing management responses (τ1). We establish the existence, uniqueness, and positivity of solutions, then analyze equilibrium stability through linearization and Lyapunov–Razumikhin functions. The characteristic equation reveals Hopf bifurcations at critical delay thresholds. Numerical simulations across 1600 parameter combinations using MATLAB R2023b’s DDE23 algorithm quantify these transitions. The results show a critical threshold near 1.64 years (20 months): below this value, systems converge to a stable equilibrium, while above it, persistent oscillations emerge within 20–26 year periods. Unexpectedly, one large delay destabilizes less than two moderate delays summing to the same total, contradicting uniform improvement strategies. Convergence to limit cycles requires roughly 40 years, exceeding typical management horizons and potentially masking true system dynamics. The critical threshold lies within realistic administrative timescales, suggesting that institutional delays may substantially contribute to observed population fluctuations. These findings indicate that accelerating either monitoring or decision processes rather than providing modest improvements to both could better stabilize exploited resources.