Demand-induced regime shift in fishery: A mathematical perspective

Abstract

Though overfishing and climate change are the primary reasons for a regime shift in the fishery, we demonstrate here a different reason for the regime shift, not reported earlier to the best of our knowledge. We show that high demand for fish may cause a regime shift in a fishery in a shorter time. For this, a four-dimensional bioeconomic fishery model is considered and analyzed to explore the system's dynamic behavior. The objective is to demonstrate how increasing demand may cause a catastrophic change in the fish and fishery. We provide the local and global stabilities of different equilibrium points, guaranteeing the stable coexistence of ecological and economic states. Our bifurcation analysis revealed that the demand parameter might play positive and negative roles in the system dynamics. Demand can make an unstable fishery stable. It can also help remove the infection from the system. On the flip side, high demand may cause a regime shift from a harvested state to a non-harvested state, making the price unbounded. Using Pontryagin's maximum principle, we further discussed optimal revenue generation.

Keywords: Fishery model; Local and global stability; Nonlinear demand; Optimal tax; Regime shift; Saturated catch.