The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect
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 para...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/290 |
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| author | Muhammad Sajjad Shabbir Qamar Din Wafa F. Alfwzan Manuel De la Sen |
| author_facet | Muhammad Sajjad Shabbir Qamar Din Wafa F. Alfwzan Manuel De la Sen |
| author_sort | Muhammad Sajjad Shabbir |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T06:56:52Z |
| format | Article |
| id | doaj.art-d5e5216a5d1c4d9b968a658c2404b815 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:56:52Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-d5e5216a5d1c4d9b968a658c2404b8152023-11-17T09:35:26ZengMDPI AGAxioms2075-16802023-03-0112329010.3390/axioms12030290The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge EffectMuhammad Sajjad Shabbir0Qamar Din1Wafa F. Alfwzan2Manuel De la Sen3Department of Mathematics, University of Poonch Rawalakot, Rawalakot 12350, PakistanDepartment of Mathematics, University of Poonch Rawalakot, Rawalakot 12350, PakistanDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment 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, SpainThe 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.https://www.mdpi.com/2075-1680/12/3/290predator–preybifurcationstabilityhost–parasitoidchaos controlchaotic behavior |
| spellingShingle | Muhammad Sajjad Shabbir Qamar Din Wafa F. Alfwzan Manuel De la Sen The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect Axioms predator–prey bifurcation stability host–parasitoid chaos control chaotic behavior |
| title | The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect |
| title_full | The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect |
| title_fullStr | The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect |
| title_full_unstemmed | The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect |
| title_short | The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect |
| title_sort | qualitative analysis of host parasitoid model with inclusion of spatial refuge effect |
| topic | predator–prey bifurcation stability host–parasitoid chaos control chaotic behavior |
| url | https://www.mdpi.com/2075-1680/12/3/290 |
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