Predator-prey models with non-analytical functional response

被引:12
作者
Kooij, Robert E. [1 ,2 ]
Zegeling, Andre [3 ]
机构
[1] Singapore Univ Technol & Design, Ctr Res Cybersecur, iTrust, 8 Somapah Rd, Singapore 487372, Singapore
[2] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, Delft, Netherlands
[3] Guilin Univ Aerosp Technol, Jinji Rd 2, Guilin, Peoples R China
关键词
Generalized Gause model; Functional response; Limit cycles; SYSTEM; BIFURCATION; UNIQUENESS; CYCLES;
D O I
10.1016/j.chaos.2019.03.036
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we study the generalized Gause model, with a logistic growth rate for the prey in absence of the predator, a constant death rate for the predator and for several different classes of functional response, all non-analytical. First we consider the piecewise-linear functional response of Holling type I, which essentially has a linear functional response on a bounded interval and a constant functional response for large enough prey density. Next we consider differentiable modifications of this type of functional response, one being a concave down function, the other one being a sigmoidal function. Our main interest is the number of closed orbits of the systems under consideration and the global stability of the system. We compare the generalized Gause model with a functional response that is nonanalytical with the generalized Gause model with a functional response that is analytical (e.g., Holling type II or III) and show that the behaviour in the first case is more complicated. As examples of this more complicated behaviour we mention: the co-existence of a stable equilibrium with a stable limit cycle and the existence of a family of closed orbits. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码:163 / 172
页数:10
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