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

Brahampal Singh ^[3] | Sunita Gakkhar ^[2]

Abstract: 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.

Keywords: Food web, Hopf bifurcation, limit cycle, persistence

Edition: Volume 5 Issue 7, July 2016,

Pages: 568 - 574

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

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