Dian Savitri, Hasan Panigoro
This article discusses the one-prey, one-predator, and the super predator model with different types of functional response. The rate of prey consumption by the predator follows Holling type I functional response and the rate of predator consumption by the super predator follows Holling type II functional response. We identify the existence and stability of critical points and obtain that the extinction of all population points is always unstable, and the other two are conditionally stable i.e., the super predator extinction point and the co-existence point. Furthermore, we give the numerical simulations to describe the bifurcation diagram and phase portraits of the model. The bifurcation diagram is obtained by varying the parameter of the conversion rate of predator biomass into a new super-predator which gives forward and Hopf bifurcation. The forward bifurcation occurs around the super predator extinction point while Hopf bifurcation occurs around the interior of the model. Based on the terms of existence and numerical simulation, we confirm that the conversion rate of predator biomass into a new super-predator controls the dynamics of the system and maintains the existence of predator. © 2020 Author(s).
Jurusan Matematika, Universitas Negeri Surabaya, Surabaya, 60292, Indonesia; Jurusan Matematika, Universitas Negeri Gorontalo, Bone Bolango, 96119, Indonesia; Jurusan Matematika, Universitas Brawijaya, Malang, 65145, Indonesia
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