Modeling the dynamics of stage-structure predator-prey system with Monod-Haldane type response function

A stage-structure predator prey model is proposed and analyzed in this paper in which predators are divided into juvenile and mature predators using Monod-Haldane-type response function. The dynamical behavior of this system both analytically and numerically is investigated from the view point of stability and bifurcation. We investigate global stability around the interior equilibrium point E* by constructing suitable Lyapunov function. Our model simulation indicates that the conversion of prey population to juvenile predators can destabilize the model system which lead to limit cycle oscillations. We also investigate that the rate of juvenile predators becoming mature predators play an important role to destabilize the model system for the stable coexistence of both the populations. We carried out extensive numerical simulations of the model to confirm the analytical findings.