Stability of a stage-structure Rosenzweig-MacArthur model incorporating Holling type-II functional response

9th Annual Basic Science International Conference 2019

自然科学（总论）

Beay, Lazarus Kalvein^1^2 ; Suryanto, Agus^1 ; Darti, Isnani^1 ; Trisilowati^1

Department of Mathematics, University of Brawijaya, East Java, Malang, Indonesia^1

Department of Education and Culture, Provincial Government of Moluccas, Indonesia^2

关键词: Equilibrium point;    Holling type II functional response;    Local stability;    Predation rates;    Reduction rate;    Routh-Hurwitz criterion;    Stage structure;    Trivial equilibrium;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/546/5/052017/pdf
DOI  :  10.1088/1757-899X/546/5/052017

学科分类：自然科学（综合）

来源: IOP

【 摘 要 】

The local stability of the Rosenzweig-MacArthur predator-prey system with Holling type-II functional response and stage-structure for prey is studied in this paper. It is shown that the model has three equilibrium points. The trivial equilibrium point is always unstable while two other equilibrium points, i.e., the predator extinction point and the coexistence point, are conditionally stable. When the predation process on prey increases, the number of predator increases. If the predation rate is less than or equal to the reduction rate of the predator, then the predator will go to extinct. By using the Routh-Hurwitz criterion, the local stability of the interior equilibrium point is investigated. It is also shown that the model undergoes a Hopf-bifurcation around the coexisting equilibrium point. The dynamics of the system are confirmed by some numerical simulations.