HOPF bifurcation Dynamics and Persistence of Two Mutually Interdependent Predator Species for Sharing a Single Prey Species under Kolmogorov Constraints

In research paper [2] we investigated local and global stability of a model consisting of two mutually interdependent predator species feeding on a single prey species. In this paper we investigated Hopf bifurcation, quasiperiodic behavior and persistence of the nonlinear ode system [2] under the Kolmogorov conditions. Both the predator species has symbiotic interaction that is mutually beneficial [2]. The existence of Hopf bifurcation is investigated and limit cycles are obtained. It is observed that the persistence is possible in the form of periodic cycle in the positive octant.