A Mathematical Analysis of Nonlinear Predator-Prey System with Poaching Effect

In this article, we have employed mathematical analysis and numerical simulations of a predator-prey model to describe the effect of predation on the prey and the predator species. The model incorporates the nonlinear functional response, the consequence of poaching of both species, and the effect of migration on the predator species in the ecosystem of Sundarbans, the largest mangrove forest in the world. In this investigation, we have developed the results concerning the boundedness, the existence and the uniqueness of the solution obtained. Furthermore, we have reflected on the Routh-Hurwitz criterion to set up the results of the local and the global stabilities respectively. We have also established the Hopf-bifurcation to view the existence of a branch of nontrivial periodic solutions. Moreover, a novel idea has been introduced by adding the poaching effect and the oscillation of the migration of the predator to the model which ultimately forms a non-autonomous one. Finally, numerical simulations have been performed to validate the analytical findings.