THE EFFECTS OF HARVESTING AND TIME DELAY ON PREDATOR-PREY SYSTEMS WITH HOLLING TYPE II FUNCTIONAL RESPONSE.

In this paper, the effects of harvesting and time delay on two different types of predator-prey systems with delayed predator specific growth and Holling type II functional response are studied by applying the normal form theory of retarded functional differential equations developed by Faria andMagalhãaes [ J. Differential Equations, 122 (1995), pp. 181-200, J. Differential Equations, 122 (1995), pp. 201-224]. Hopf bifurcations are demonstrated in models with harvesting of the prey at a constant rate by taking the delay as a bifurcation parameter, and numerical examples supporting our theoretical prediction are also given. Furthermore, bifurcation analysis indicates that delayed predator-prey systems with predator harvesting exhibit Bogdanov-Takens bifurcation. The versal unfoldings of the models at the Bogdanov-Takens singularity are obtained, and numerical simulations and bifurcation diagrams are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]