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Global stability and sliding bifurcations of a non-smooth Gause predator–prey system

Global stability and sliding bifurcations of a non-smooth Gause predator–prey system

Yang, Jin, Tang, Sanyi and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2013) Global stability and sliding bifurcations of a non-smooth Gause predator–prey system. Applied Mathematics and Computation, 224. pp. 9-20. ISSN 0096-3003 (doi:https://doi.org/10.1016/j.amc.2013.08.024)

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Abstract

A non-smooth Gause predator–prey model with a constant refuge is proposed and analyzed. Firstly, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between the existence of a regular equilibrium and a pseudo-equilibrium are studied, and the results indicate that the two types of equilibria cannot coexist. The sufficient and necessary conditions for the global stability of limit cycle, sliding touching cycle, canard cycle, focus point and pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Furthermore, sliding bifurcations related to boundary node (focus) and touching bifurcations were investigated by employing theoretical and numerical techniques. Finally, we compare our results with previous studies on a non-smooth Gause predator–prey model without involving a carrying capacity for the prey population, and some biological implications are discussed.

Item Type: Article
Uncontrolled Keywords: Filippov system, Refuge, Limit cycle, Canard cycle, Sliding bifurcation
Subjects: S Agriculture > S Agriculture (General)
S Agriculture > SF Animal culture
Faculty / Department / Research Group: Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Faculty of Engineering & Science > Natural Resources Institute
Last Modified: 03 Oct 2013 16:07
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/10291

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