Effect of discontinuous harvesting on a diffusive predator-prey model

Abstract The management of predator-prey systems, particularly those with discontinuous harvesting, plays a crucial role in maintaining ecological balance and ensuring the sustainable use of renewable resources. Despite the importance of this topic, the dynamics of diffusive predator-prey models with discontinuous harvesting have not been thoroughly explored in existing literature. This study addresses this gap by investigating a diffusive predator–prey model incorporating a discontinuous harvesting function. We establish the existence and boundedness of solutions, analyse the conditions under which a positive steady state is achieved, and explore the model’s stability, including global asymptotic stability and convergence in finite time. Additionally, we examine the effects of Turing instability, Hopf bifurcation, and steady-state bifurcation within the model. Numerical simulations are provided to illustrate the impact of discontinuous harvesting on the system’s dynamics, highlighting the practical applications of the theoretical results in fields such as pest control. The findings of this study offer valuable insights for the design of effective population management strategies in ecological and agricultural contexts.