Neimark-Sacker bifurcation and stability of a prey-predator system

In this paper, we investigate the stability and bifurcation of a discrete-time prey-predator system which is subject to an efficiency of prey conversion into predators and minimum threshold prey consumption required before predators begin to reproduce. It is concluded that the system undergoes Neima...

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Published inMathematical notes (Miskolci Egyetem (Hungary)) Vol. 21; no. 2; pp. 873 - 885
Main Author Gümüş, Özlem Ak
Format Journal Article
LanguageEnglish
Published Miskolc University of Miskolc 2020
Subjects
Bifurcations
Discrete time systems
Predator-prey simulation
Predators
Stability
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Summary:In this paper, we investigate the stability and bifurcation of a discrete-time prey-predator system which is subject to an efficiency of prey conversion into predators and minimum threshold prey consumption required before predators begin to reproduce. It is concluded that the system undergoes Neimark-Sacker bifurcations in a small neighborhood of the unique positive equilibrium which depends on the number of prey-predator. Moreover, the numerical simulations are done to demonstrate the theoretical results.
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ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2020.3386