Analysis stability of predator-prey model with Holling type I predation response function and stage structure for predator

Abstract

Abstract This paper developed mathematical models with structural stages from predators, namely small predators and adult predators. The predation function of adult predators follows the Holling I response function according to the characteristics in the ecosystem. In this model, an analysis of the equilibrium value and stability of the interior equilibrium value is carried out. Analysis of the stability of interior equilibrium values with the system linearization method at the value of equilibrium. Four equilibrium values were realized. Each equilibrium value has its own characteristics and conditions. The stability characteristics of equilibrium values were obtained using the Routh-Hurwitz criteria. Also, consider the eigenvalue of the characteristic equation in the Jacobi matrix. We also identify population changes made with cases that allow the ecosystem to work.