Coupled Ecological-Economic Feedbacks in a Polluted Fishery: Threshold Dynamics, Hysteresis, and Sustainable Harvesting

Freshwater fisheries are increasingly threatened by environmental pollution and growing market demand, requiring management strategies that balance ecological sustainability with economic returns. We develop a bioeconomic fishery model for a polluted lake that integrates fish population dynamics, environmental pollution, adaptive harvesting effort, endogenous fish price, pollution-control investment, and policy-regulated harvesting-cost control within a unified ecological-economic framework. The model exhibits multiple stable states, including sustainable harvesting, harvesting-free, and fish-extinction regimes. A critical pollution-input threshold is identified beyond which the fish-extinction equilibrium becomes locally stable, indicating an increased risk of population collapse. Increasing pollution induces bistability, whereas sufficiently high market demand destabilizes the coexistence equilibrium through a Hopf bifurcation, producing persistent oscillations. The interaction between pollution and market demand further generates hysteresis, implying that restoring degraded fisheries requires substantially stronger interventions than preventing collapse. Treating the policy-regulated harvesting cost as the control variable, we derive an optimal harvesting policy consisting of a bang-bang phase followed by a singular control that maximizes the long-term harvesting revenue. Overall, our results demonstrate that coupled ecological-economic feedbacks can generate tipping points, oscillatory dynamics, and path-dependent transitions, highlighting the importance of integrated pollution control, harvesting regulation, and economic incentives for sustainable fishery management.