Stability Analysis and Numerical Simulation of Prey-Predator System with Age Structure

Abstract

This study developed a four-dimensional prey-predator model consisting four groups, i.e. immature prey, mature prey, immature predator, and mature predator. The reproduction of the prey depends on the mature group. Only mature predators take part in predation and prefer to consume mature prey populations. Analysis on the system by determining the equilibrium point of the prey-predator model. The results of the stability analysis obtained three equilibrium point i.e. the extinction of all species, the extinction of predator, and the existence of all species. Stability of model is analyzed based on the eigenvalues of the Jacobian matrix and by using Routh's criteria. Numerical simulations are carried out to confirm analytical results.  Furthermore, numerical simulation by different parameter is provided. There are three cases at the equilibrium point of the existence of all species where the parameters  and  are different. The results show that  the prey and predator populations will be stable or will not experience extinction for the all species equilibrium point.