Effects of population density on prey-predator system stability

Abstract

The prey-predator model is explained by considering the population densities of both immature and mature prey and predators. The models were divided into two cases: the absence of the mature prey population density and the absence of the immature predator population density. These models were then analyzed around the eiop[quilibrium point, with the stability determined based on the eigenvalues of the Jacobian matrix. Stability analysis was also performed using Routh’s criteria. Furthermore, numerical simulations confirmed the analytical results of the model. The dependence on parameters in each case was investigated for extreme values. Based on the analytical results and numerical simulations, it can be concluded that the equilibrium point is always stable whenever it exists. Thus, the populations of immature and mature prey, as well as immature and mature predators, will not undergo extinction.