Coupled Ecological-Economic Feedbacks in a Polluted Fishery: Threshold Dynamics, Hysteresis, and Sustainable Harvesting
- 1Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
- 2Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Puttaparthi 515134, India
- 3Institute of Mathematics, Czech Academy of Sciences, Branch in Brno, 61662 Brno, Czech Republic
Abstract
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.
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BibTeX
@article{maity2026coupled,
title = {{Coupled Ecological-Economic Feedbacks in a Polluted Fishery: Threshold Dynamics, Hysteresis, and Sustainable Harvesting}},
author = {Sourav Maity and Santanu Bhattacharya and Robert Hakl and Nandadulal Bairagi},
journal = {Mathematics},
year = {2026},
month = sep,
doi = {10.3390/math14193444},
url = {https://www.mdpi.com/2227-7390/14/19/3444},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Coupled Ecological-Economic Feedbacks in a Polluted Fishery: Threshold Dynamics, Hysteresis, and Sustainable Harvesting
AU - Sourav Maity
AU - Santanu Bhattacharya
AU - Robert Hakl
AU - Nandadulal Bairagi
PY - 2026
DA - 2026/09/22
JO - Mathematics
DO - 10.3390/math14193444
UR - https://www.mdpi.com/2227-7390/14/19/3444
AB - 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.
SN - 2227-7390
ER -