Period-doubling bifurcation of a discrete metapopulation model with a delay in the dispersion terms

In this work the period-doubling bifurcation of a discrete metapopulation with delay in the dispersion terms is discussed. By using the central manifold method, the period-doubling bifurcation can be analyzed from the viewpoint of the dynamical system. Intensive simulation on this model shows the dynamics of the metapopulation is similar to that of a single logistic model as the bifurcation parameter μμ increases when 0≤b<1/20≤b<1/2, where bb is the dispersion parameter.