Predator-prey models with non-analytical functional response
| Autor: | Robert E. Kooij, André Zegeling |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Concave function
General Mathematics Applied Mathematics Functional response General Physics and Astronomy Statistical and Nonlinear Physics Generalized Gause model 01 natural sciences 010305 fluids & plasmas Limit cycles Limit cycle Bounded function Linear form 0103 physical sciences Quantitative Biology::Populations and Evolution Applied mathematics Differentiable function Logistic function Constant (mathematics) 010301 acoustics Mathematics |
| Zdroj: | Chaos, Solitons & Fractals, 123 |
| ISSN: | 0960-0779 |
| DOI: | 10.1016/j.chaos.2019.03.036 |
| Popis: | 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 non-analytical 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. |
| Databáze: | OpenAIRE |
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