The impact of provision of additional food to predator in predator–prey model with combined harvesting in the presence of toxicity

摘要

In this article, the global dynamics of a predator–prey system incorporating combined harvesting has been investigated. The additional food is being provided to the predator, accordingly, modified Holling type-II functional response is considered in the model. The presence of toxicants affect the quality of food for both the species, reducing their growth. The steady states of the system are obtained under some suitable conditions. The local and global dynamics are explored. The conditions for permanence and existence for bionomic equilibrium of the system have been investigated. It is also observed that the system exhibits local bifurcations i.e., transcritical, Hopf, saddlenode as well as global bifurcations i.e., Bogdanov–Takens bifurcation and generalized Hopf bifurcation with respect to the suitable set of parameters. Optimal harvesting policy is discussed with the help of Pontryagin's maximum principle to preserve both the species from extinction and maintain a sustainable fishery. Numerical simulations are carried out for the suitable choice of parameters.