Nonlinear behavior of the parameterized Logistic differential systems

This paper deals with local stability, Hopf bifurcation and chaos in the parameterized Logistic differential systems with delay. By applying the Halanay inequality, the local stability of the Logistic differential systems is discussed. The stability of bifurcation periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. In the end, interesting nonlinear behavior of the parameterized Logistic differential systems with a single parameter delay is detected by numerical examples.