Bifurcation analysis and chaos control for fractional predator-prey model with Gompertz growth of prey population.
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| Title: | Bifurcation analysis and chaos control for fractional predator-prey model with Gompertz growth of prey population. |
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| Authors: | Almatrafi, Mohammed Bakheet1 (AUTHOR) mmutrafi@taibahu.edu.sa, Berkal, Messaoud2,3 (AUTHOR) mb299@gcloud.ua.es |
| Source: | Modern Physics Letters B. 8/20/2025, Vol. 39 Issue 23, p1-29. 29p. |
| Subjects: | Gompertz functions (Mathematics), Caputo fractional derivatives, Bifurcation theory, Bifurcation diagrams |
| Abstract: | This paper discusses a fractional-order prey–predator system with Gompertz growth of prey population in terms of the Caputo fractional derivative. The non-negativity and boundedness of the solutions of the considered model are successfully analyzed. We utilize the Mittag-Leffler function and the Laplace transform to prove the boundedness of the solutions of this model. We describe the topological categories of the fixed points of the model. It is theoretically demonstrated that under certain parametric conditions, the fractional-order prey–predator model can undergo both Neimark–Sacker and period-doubling bifurcations. The piecewise constant argument approach is invoked to discretize the considered model. We also formulate some necessary conditions under which the stability of the fixed points occurs. We find that there are two fixed points for the considered model which are semi-trivial and coexistence fixed points. These points are stable under some specific constraints. Using the bifurcation theory, we establish the Neimark–Sacker and period-doubling bifurcations under certain constraints. We also control the emergence of chaos using the OGY method. In order to guarantee the accuracy of the theoretical study, some numerical investigations are performed. In particular, we present some phase portraits for the stability and the emergence of the Neimark–Sacker and period-doubling bifurcations. The biological meaning of the given bifurcations is successfully discussed. The used techniques can be successfully employed for other models. [ABSTRACT FROM AUTHOR] |
| Copyright of Modern Physics Letters B is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 185308963 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Bifurcation analysis and chaos control for fractional predator-prey model with Gompertz growth of prey population. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Almatrafi%2C+Mohammed+Bakheet%22">Almatrafi, Mohammed Bakheet</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mmutrafi@taibahu.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Berkal%2C+Messaoud%22">Berkal, Messaoud</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> mb299@gcloud.ua.es</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Modern+Physics+Letters+B%22">Modern Physics Letters B</searchLink>. 8/20/2025, Vol. 39 Issue 23, p1-29. 29p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Gompertz+functions+%28Mathematics%29%22">Gompertz functions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+diagrams%22">Bifurcation diagrams</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper discusses a fractional-order prey–predator system with Gompertz growth of prey population in terms of the Caputo fractional derivative. The non-negativity and boundedness of the solutions of the considered model are successfully analyzed. We utilize the Mittag-Leffler function and the Laplace transform to prove the boundedness of the solutions of this model. We describe the topological categories of the fixed points of the model. It is theoretically demonstrated that under certain parametric conditions, the fractional-order prey–predator model can undergo both Neimark–Sacker and period-doubling bifurcations. The piecewise constant argument approach is invoked to discretize the considered model. We also formulate some necessary conditions under which the stability of the fixed points occurs. We find that there are two fixed points for the considered model which are semi-trivial and coexistence fixed points. These points are stable under some specific constraints. Using the bifurcation theory, we establish the Neimark–Sacker and period-doubling bifurcations under certain constraints. We also control the emergence of chaos using the OGY method. In order to guarantee the accuracy of the theoretical study, some numerical investigations are performed. In particular, we present some phase portraits for the stability and the emergence of the Neimark–Sacker and period-doubling bifurcations. The biological meaning of the given bifurcations is successfully discussed. The used techniques can be successfully employed for other models. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Modern Physics Letters B is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0217984925501039 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: 1 Subjects: – SubjectFull: Gompertz functions (Mathematics) Type: general – SubjectFull: Caputo fractional derivatives Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Bifurcation diagrams Type: general Titles: – TitleFull: Bifurcation analysis and chaos control for fractional predator-prey model with Gompertz growth of prey population. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Almatrafi, Mohammed Bakheet – PersonEntity: Name: NameFull: Berkal, Messaoud IsPartOfRelationships: – BibEntity: Dates: – D: 20 M: 08 Text: 8/20/2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02179849 Numbering: – Type: volume Value: 39 – Type: issue Value: 23 Titles: – TitleFull: Modern Physics Letters B Type: main |
| ResultId | 1 |
