The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect

Author:

Shabbir Muhammad Sajjad1ORCID,Din Qamar1ORCID,Alfwzan Wafa F.2ORCID,De la Sen Manuel3ORCID

Affiliation:

1. Department of Mathematics, University of Poonch Rawalakot, Rawalakot 12350, Pakistan

2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

3. Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, Campus of Leioa (Bizkaia), University of the Basque Country, 48940 Leioa, Spain

Abstract

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an attack of parasitoids. We found the parametric factors affecting the existence of the equilibrium points and uniqueness of equilibrium points. A local stability analysis of host–parasitoid models was also carried out. Bifurcation theory was used to observe that the host–parasitoid models undergo Neimark–Sacker bifurcation. The effect of the existence of constant refuge effect on the local stability and bifurcation of models was also explored. Hybrid chaos control methodology was used to control the chaotic behavior of model. In addition, numerical simulations, bifurcation diagrams, and phase portraits of the models are also presented.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference26 articles.

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2. Neimark–Sacker bifurcation and stability of a certain class of host-parasitoid models with host refuge effect;Mujic;Int. J. Bifurc. Chaos,2020

3. Stability of a certain class of a host-parasitoid model with a spatial refuge effect;Mujic;J. Biol. Dyn.,2020

4. Global qualitative analysis of a discrete host-parasitoid model with refuge and strong Allee effects;Wu;Math. Methods Appl. Sci.,2018

5. Controlling chaos and Neimark-Sacker bifurcation in a host-parasitoid model;Din;Asian J. Control.,2019

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1. Dynamic Complexities in Competing Parasitoid Species on a Shared Host;International Journal of Bifurcation and Chaos;2024-02

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