Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator

Abstract

In the present work, we investigate on the dynamics of predator–prey model with prey refuge in proportion to both species and the effect of additional food provided to the predator. A Holling type II functional response in presence of additional food is taken to represent the interaction between prey and predator. Positivity and uniform boundedness of the solutions of the system are discussed analytically. Existence of equilibrium points and their stability criteria are analysed. Condition for occurrence of Hopf-bifurcation is derived analytically. It is found that the consumption rate of predator plays an important role in the dynamics of present system. Also, discrete time lag (gestation delay) in the proposed model is incorporated to observe the switching behaviour of the delay parameter through Hopf-bifurcation. Moreover, this work aims to analyse the dynamical behaviour of the considered predator–prey model when the predator is harvested at a constant rate. Numerical simulations are performed to verify all the analytical results using MATLAB and MATCONT.