Stability Analysis of Predator-Prey Model

This paper analyzed the stability of the predator-prey model by using the original Lotka-Volterra predator-prey model, which consists of two ordinary differential equations and describes the interaction between predator populations and prey populations. This study solved the equilibrium points and analyzed the stability on this basis. The specific steps were constructing a Jacobian matrix to replace nonlinear systems with linear approximations and substituting the equilibrium points into it. After obtaining the Jacobian matrix with specific values, we calculated its eigenvalue. According to the theory of linear stability, which says the sign of the real part of the eigenvalue determines the type of equilibrium points, we performed a stability analysis. The result of this study proved that the trivial equilibrium point is a saddle point and thus is unstable. In contrast, the non-trivial equilibrium point is neutrally stable, for it is a center. By using the method of numerical simulation, we verified the conclusion and visually showed the nature of the periodic oscillation of the Lotka-Volterra system.