Research ArticlesNo Access

Dynamics and bifurcations of a host–parasite model

Ali Atabaigi

Department of Mathematics, Razi University, Kermanshah, Iran

E-mail Address: aliaelmi@gmail.com

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and

Mohammad Hossein Akrami

Department of Mathematical Sciences, Yazd University, Yazd, Iran

E-mail Address: akrami@yazd.ac.ir

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https://doi.org/10.1142/S1793524517500899Cited by:8 (Source: Crossref)

Abstract

A two-parameter family of discrete models, consisting of two coupled nonlinear difference equations, describing a host–parasite interaction is considered. In particular, we prove that the model has at most one nontrivial interior fixed point which is stable for a certain range of parameter values and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter.

Keywords:

AMSC: 92D25, 34D05, 34C23

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