Bifurcation in a Discrete Two Patch Logistic Metapopulation Model

In this paper, local bifurcation of a discrete two patch logistic metapopulation is discussed. By the central manifold method, flip bifurcation can be analyzed at the positive fixed point from the viewpoint of the dynamical system, and the system can not undergo a fold bifurcation. Simulations on this model show the discrete model can have rich dynamical behaviors. The state feedback control is done to stabilize chaotic orbits at an unstable fixed point. Then the eigenvalues of the corresponding diffusion system with Dirichlet boundary conditions are found for future bifurcation analysis. Key–Words: Logistic metapopulation, Flip bifurcation, Fold bifurcation, Central manifold, State feedback control, Eigenvalue