Dynamics of a Filippov predator-prey system with stage-specific intermittent harvesting

Journal article, 2021

The invasion of Indo-Pacific lionfish (Pterois volitans) together with unsustainable harvesting of herbivorous fish has caused major ecological changes in the western Atlantic and Caribbean coral reefs. Developing an effective harvesting policy of herbivorous reef fish and the invasive lionfish is necessary to minimize the adverse ecological impacts. To evaluate the potential efficacy of controlling the growth of lionfish population, we have proposed a non-smooth two-stage-structured mathematical model with two harvesting policies (non-selective and selective) of lionfish determined by a control function with a discontinuity at a critical herbivorous fish density. We study the sliding mode dynamics of the Filippov system, the boundary equilibrium bifurcation, and the pseudo-saddle-node bifurcation. We use threshold harvesting with hysteresis that helps in preventing the collapse of the herbivorous fish population through a bounded oscillation about pseudo-equilibrium. Our results show that a longer herbivorous fish harvesting period can be achieved in selective harvesting policy without compromising the herbivorous fish stock.