Effect of prey refuge in a tri-trophic food chain model with Monod-Haldane type response function

The present paper deals with the control of a constant proportion of prey refuge in the presence of infra-specific competition among adult predator species of a continuous time food chain model. Dynamic behaviour of the model close to the biologically meaningful feasible equilibria is examined in detail. The preliminary results such as positivity and boundedness of the proposed system are well-recognized. Stability analysis together with the local and global stability of the equilibria has been carried out in order to scrutinize the behaviour of the system. The Hopf-bifurcation analysis of the model with respect to the significant parameter has been explored both analytically and numerically. The effects of the prey refuge parameters on the dynamical behaviour of the system are displayed through a number of valid figures. Also, effects of intra-specific competition among adult predators on the system are exposed by different diagrams. Such outcomes can be exercised to recover ecological decision-making on species protection.