Stability and bifurcation analysis of a discrete-time host-parasitoid model with Holling III functional response

We study the dynamical properties of a discrete-time host-parasitoid model with Holling type III functional response. It is shown that flip bifurcation and Neimark-Sacker bifurcation occur in certain parameter regimes. A sufficient condition based on the model parameters for which both populations c...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 10; pp. 22675 - 22692
Main Authors Liu, Xijuan, Liu, Yun
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
boundedness
host-parasitoid model
mode-locking structures
neimark-sacker bifurcation
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Summary:We study the dynamical properties of a discrete-time host-parasitoid model with Holling type III functional response. It is shown that flip bifurcation and Neimark-Sacker bifurcation occur in certain parameter regimes. A sufficient condition based on the model parameters for which both populations can coexist is derived. The boundedness, existence and local stability of the unique equilibrium are proved. In addition, the numerical simulations have been done, in addition to supporting the analytical findings, more behaviors are extracted from the model in a two-dimensional parameter space. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete model.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231154