Limit Cycle in a Herbivore-Plant-Bee Model Containing a Time Delay

The dynamical behavior of time delay herbivore-plant-pollinator ecosystem is studied. The time delay arises from the fact that it takes time for a pollinated flower to develop into a new plant. A dynamical analysis is used to show that a stable steady state undergoes a Hopf bifurcation to a limit cycle behavior as the delay time crosses a critical value. This prediction is verified by numerically solving the set of first order differential equations.