Bifurcation Analysis on Prey & Predator Model: Study on Both 2nd and 3rd Type of Holing Response Functions
Gusrian Putra (a*), Dear Michiko Mutiara Noor (a), Yuslenita Muda (b), Lidya Manurung (a)

a) Dept. Mathematics, Faculty of Sciences, Institut Teknologi Sumatera
Jl. Terusan Ryacudu, Way Huwi, Kec. Jati Agung, Kabupaten Lampung Selatan, Lampung 35365, Indonesia
*gusrian.putra[at]ma.itera.ac.id
b) Dept. Mathematics, Faculty of Sciences and Technology, Universitas Islam Negeri Syarif Kasim Riau
Jl. HR. Soebrantas No.Km. 15, RW.15, Simpang Baru, Kota Pekanbaru, Riau 28293

Abstract

The Prey-Predator model involving Holling Type-II and Holling Type-III is investigated in detail in this paper. We begin our study by showing the positivity and boundedness of its positive solutions. The equilibria are calculated and their stability behavior are determined by means of linear stability analysis. Global stability of one of the equilibria, i.e., the interior equilibrium is investigated by means of Lyapunov function. We also provide the study of bifurcation in the model regarding the involvement of the Holling terms.

Keywords: Prey-Predator mode, Holling term, Stability, Lyapunov function, bifurcation

Topic: Minisymposia Dynamical Systems