Bifurcations and chaotic behavior of a predator-prey model with discrete time

In this paper, the dynamical behavior of a predator-prey model with discrete time is discussed in terms of both theoretical analysis and numerical simulation. The existence and stability of four equilibria are analyzed. It is proved that the system undergoes Flip bifurcation and Hopf bifurcation around its unique positive equilibrium point using center manifold theorem and bifurcation theory. Additionally, by applying small perturbations to the bifurcation parameter, chaotic cases occur at some corresponding internal equilibria. Finally, numerical simulations are provided with the help of maximum Lyapunov exponent and phase diagrams, which reveal a complex dynamical behavior.

Automated summary

In this paper, the dynamical behavior of a predator-prey model with discrete time is explored through theoretical analysis and numerical simulation. The existence and stability of four equilibria are analyzed, with Flip bifurcation and Hopf bifurcation occurring at the unique positive equilibrium point. Chaotic cases are observed at some corresponding internal equilibria when small perturbations are applied to the bifurcation parameter. Numerical simulations using maximum Lyapunov exponent and phase diagrams reveal a complex dynamical behavior.