Qualitative Analysis of an Additional Food Provided Predator–Prey Model in the Presence of Allee Effect (original) (raw)

2017, International journal of applied and computational mathematics

The present paper analyzes a predator-prey model in which the predator is provided with additional food and subjected to Allee effect. The conditions for the existence of equilibrium points and their local stability have been investigated. Under certain conditions, it is found that the solutions depend highly on the initial values. The existence of the bifurcations such as Bogdanov-Takens, Hopf-Andronov, Transcritical and Saddle-node, for the system have been shown. Further, the appearance of homoclinic loop, emerging through Hopf-bifurcation has been shown through numerical simulation. Numerical simulations have been proposed to confirm the analytical results.