Dynamics of Prey Predator Model with Harvesting of Prey

Abstract

In this paper we studied the dynamics of prey-predator model with Holling type-II response. The predator is generalist type and can sustain in absence of prey. In addition to that a constant harvesting effort is induced in the prey species. The model is characterized by a couple of differential equations. The well posed ness of the model is established. The system is bounded, exhibits positive solutions and persistence. The possible equilibrium points are identified. The linear stability analysis is carried out at all points. Global stability is also addressed by constructing suitable Lyapunov’s functions. Numerical simulation id performed and shown that the system is globally asymptotically stable. the numerical simulations not only confirm the global asymptotic stability but also provide insights into the long-term behavior of the system under various parameter regimes. Sensitivity analysis is conducted to assess the robustness of the model to parameter variations, shedding light on key factors influencing the dynamics of the prey-predator system. Furthermore, bifurcation analysis is performed to explore the emergence of complex behaviors such as oscillations and chaos, elucidating the system's response to external perturbations. The implications of the findings are discussed in the context of ecological management and conservation efforts, highlighting the importance of understanding the intricate interactions within ecosystems for devising effective strategies. Moreover, the study underscores the significance of mathematical modeling in elucidating ecological dynamics and informing decision-making processes aimed at preserving biodiversity and ecosystem stability. Additionally, avenues for future research are outlined, including extending the model to incorporate spatial dynamics and investigating the effects of environmental variability. Overall, this comprehensive analysis provides valuable insights into the dynamics of prey-predator interactions and offers a foundation for further exploration in ecological modeling and conservation science.