Tang, Guangyao, Tang, Sanyi and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2014) Global analysis of a Holling type II predator–prey model with a constant prey refuge. Nonlinear Dynamics, 76 (1). pp. 635-647. ISSN 0924-090X (Print), 1573-269X (Online) (doi:https://doi.org/10.1007/s11071-013-1157-4)

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Abstract

A global analysis of a Holling type II predator–prey model with a constant prey refuge is presented. Although this model has been much studied, the threshold condition for the global stability of the unique interior equilibrium and the uniqueness of its limit cycle have not been obtained to date, so far as we are aware. Here we provide a global qualitative analysis to determine the global dynamics of the model. In particular, a combination of the Bendixson–Dulac theorem and the Lyapunov function method was employed to judge the global stability of the equilibrium. The uniqueness theorem of a limit cycle for the Lineard system was used to show the existence and uniqueness of the limit cycle of the model. Further, the effects of prey refuges and parameter space on the threshold condition are discussed in the light of sensitivity analyses. Additional interesting topics based on the discontinuous (or Filippov) Gause predator–prey model are addressed in the discussion.

Item Type:	Article
Uncontrolled Keywords:	global analysis, refuge, limit cycle, uniqueness, nonsmooth predator–prey model
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > Natural Resources Institute Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Last Modified:	18 Oct 2016 09:14
URI:	http://gala.gre.ac.uk/id/eprint/10818

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