Dynamics analysis of a coupled fishery-economic model with environmental fluctuations

Human activities and climate change are severely destabilizing fishery ecosystems globally, leading to a significant reduction in biodiversity, adversely affecting the global fishery market, and resulting in substantial economic losses. To better understand the intrinsic mechanism of interaction between fishery ecology and fishery market in a stochastic environment, this paper presents a stochastic fishery-economy coupled model. We establish sufficient conditions for the persistence and collapse of both the fishery resource and the fishery market, detailing three scenarios: (i) the fishery market collapses while the fishery resource remains; (ii) both the fishery resource and the market fail, and (iii) both the fishery resource and the market persist. Additionally, we estimate the probability of fishery resource collapse within a given time. To elucidate the intrinsic mechanisms by which market price and stochastic disturbances affect the fishery resource and the market, we derive the explicit local probability density of the stochastic model using Fokker-Planck equation. Our findings suggest that decision-makers can mitigate the negative impacts of stochastic environments on the fishery resource and the market by adjusting the price parameter. Interestingly, our results reveal that environmental stochasticity acts as a double-edged sword: while noise can make the fishery market vulnerable and reduce fishing pressure on resources, thereby promoting fishery resource growth, excessive noise can also directly inhibit the growth of fishery resources. Finally, we illustrate our results through numerical simulations.