Dynamics in a discrete-time predator-prey system with Allee effect
The paper investigates the dynamics of the discrete-time predator-prey system with Allee effect. The authors prove the existence and the stability of fixed points in the system. Then, based on the bifurcation theory and the center manifold theory, they derive conditions for flip bifurcation and Hopf bifurcation. Also, the existence of chaos in the sense of Maroto is shown, using both analytical and numerical methods. The rich dynamical behaviour of the system is also illustrated here by using bifurcation diagrams, phase portraits, Lyapunov exponents and fractal dimensions. It is shown that the dynamical behaviour of the system can move from the complex unstable states to the stable states as the Allee constant increases.
scientific article; zbMATH DE number 6155022