Puji Andayani, Wuryansari Muharini Kusumawinahyu
This paper concerns with a stability analysis of a three species predator-prey model, which describes interaction between prey, preda-tor, and omnivore. Some parameter combinations resulting at mostfive equilibrium points under some suffcient conditions for their existence. It can be shown that all solutions which start from positive initial condi-tions are bounded. Local stability analysis of the equilibria is performed by using standard method of ODE. The analysis results can be classified into two categories of parameters. For parameters in the first category, there is no positive equilibrium and we rigorously prove that all solution trajectories converge to the boundary equilibria. We also perform some numerical simulations to support the analytical results. For parameters in the second category, we provide some numerical simulations and find that beside global stability, chaotic phenomenon is also captured.
Mathematics Department, Brawijaya University, Jl. Veteran Malang, 65145, Indonesia
