Strong Coexistence (Local and Global Stability) of Two Mutually Interdependent Predator Species for Sharing a Single Prey Species

A model consisting of two mutually interdependent predator species feeding on a single prey species is studied. Both the predator species has symbiotic interaction that is mutually beneficial. The local stability of equilibria points is analyzed. It is observed that the persistence is possible in the form of stable non zero equilibrium point or periodic limit cycle in the positive octant. It is shown that in the case of two competing predator species feeding over a single prey species, coexistence is not possible and only the fittest will survive [7], but in the case when two predator species have mutual cooperation feeding over a single prey species, then strong coexistence (local and global stability) is possible. In this paper the mathematical model comprising two mutually interdependent predator species and a single prey species shows rich dynamics numerically as well as analytically. The effect of mutually Cooperation on the two predators feeding on a common prey was investigated.