The Bifurcation of Two Invariant Closed Curves in a Discrete Model

Abstract EN

A discrete population model integrated using the forward Euler method is investigated.

The qualitative bifurcation analysis indicates that the model exhibits rich dynamical behaviors including the existence of the equilibrium state, the flip bifurcation, the Neimark-Sacker bifurcation, and two invariant closed curves.

The conditions for existence of these bifurcations are derived by using the center manifold and bifurcation theory.

Numerical simulations and bifurcation diagrams exhibit the complex dynamical behaviors, especially the occurrence of two invariant closed curves.