Qualitative analysis in two prey-predator system with persistence

Abstract

In this work, the system with two preys and one predator population is qualitatively analyzed.  The predator exhibits a Holling type I response to one prey and a Holling type IV response to the other prey. The boundedness of the system is analyzed.  We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium (E0) and axial equilibrium (E1) , the system is found to be unstable .Also; we obtain the necessary and sufficient conditions for existence of interior equilibrium point (E*)  and local and global stability of the system at the interior equilibrium (E*) . Depending upon the existence of limit cycle, the persistence condition is established for the system. The analytical findings are illustrated through computer simulations from which we observed that, using the parameter  and it is possible to break unstable behavior of system and drive it to a stable state.