Multistability in a Leslie‐Gower–type predation model with a rational nonmonotonic functional response and generalist predators. Issue 2 (7th November 2019)

• Record Type: Journal Article
• Authors: Puchuri, Liliana; González‐Olivares, Eduardo; Rojas‐Palma, Alejandro
• Is Part Of: Computational and mathematical methods. Volume 2:Issue 2(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-07
• Subjects: bifurcation -- functional response -- limit cycle -- predator‐prey model -- separatrix curve -- stability; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1070
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : This work deals with a modified Leslie‐Gower–type model, in which two ecological issues are considered. (i) The action of predators over their prey is described by a nonmonotonic functional response, and (ii) the predators are generalists, ie, in absence of their favorite prey, they look for an alternative food. The proposed model is described by an autonomous differential equation system of Kolmogorov type, which has interesting and rich dynamics. We extend the results obtained in previous research articles, where the predators are considered specialists. It is shown that the model can have up to three positive equilibria coexisting for a wide set of parameters, one of them being a saddle point and the other can be a focus of multiplicity two. Moreover, these points can coincide to obtain a codimension‐two cusp point. Varying the parameters in a small neighborhood of the parameter values, the model undergoes the Bogdanov‐Takens bifurcation and a multiple Hopf bifurcation in the vicinities of these two equilibria, respectively. To reinforce our analytical results, numerical simulations are shown. Furthermore, graphical simulations of some properties that did not prove in the text were also added.