Analysis of a Holling II System with Frequency-dependent Fitness and Constant Harvesting Rate of Prey

We study a Holling II predator-prey model with frequency-dependent fitness and nonzero constant harvesting rate of prey. It is shown that the model has at most one hyperbolic positive equilibrium which may be a node, focus or a center and can exhibit the Hopf bifurcation or Heteroclinic bifurcation when parameters vary in a small neighborhood of the values of parameters. Meanwhile, a sufficient condition for no closed trajectory existing in system is obtained. And it is further shown that by choosing different values of parameters the model can have a stable or unstable limit cycle only enclosing the positive equilibrium. 156 Huaying Wang et al. These results reveal far richer dynamics compared to the model with no harvesting such as general Gause-type model. Mathematics Subject Classification: 92D30, 92D40, 93D20