Global dynamics of an additional food provided predator–prey system with constant harvest in predators

• Predators are provided with additional food and harvested at a constant rate.
• Provision of additional food enhances the stable and oscillatory coexistence.
• Complete global dynamics is studied with harvesting as a bifurcation parameter.
• All possible local and global bifurcation scenarios are identified.
• Bogdanov–Takens and homoclinic bifurcation indicates extinction of predators.

The article aims to study the global dynamics associated with a predator prey system when the predator is provided with additional food and harvested at a constant rate. This study supplements the existing literature on the dynamics of additional food provided predator prey system by focusing on the consequences of harvesting the predators. It presents a comprehensive view on the entire range of bifurcations that take place in the considered system and highlights the dependence of the system dynamics on its vital parameters. This study provides important tools for investigations pertaining to controllability of the system which are essential from the real world applications perspective.