Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response
This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator mod...
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| Format: | Article |
| Language: | English |
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Akif AKGUL
2024-07-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3158438 |
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| author | G.s. Mahapatra Sarker Md Sohel Rana Md. Jasim Uddin P. K. Santra |
| author_facet | G.s. Mahapatra Sarker Md Sohel Rana Md. Jasim Uddin P. K. Santra |
| author_sort | G.s. Mahapatra |
| collection | DOAJ |
| description | This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point. |
| format | Article |
| id | doaj-art-febfc1708eec46748be81d513d228f5d |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-febfc1708eec46748be81d513d228f5d2025-01-23T18:19:34ZengAkif AKGULChaos Theory and Applications2687-45392024-07-016319220410.51537/chaos.13007541971Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional ResponseG.s. Mahapatra0https://orcid.org/0000-0002-5225-0445Sarker Md Sohel Rana1https://orcid.org/0000-0002-6657-2269Md. Jasim Uddin2https://orcid.org/0000-0001-7503-481XP. K. Santra3https://orcid.org/0000-0002-1857-135XNational Institute of Technology PuducherryUniversity of DhakaUniversity of DhakaAbada Nsup SchoolThis paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point.https://dergipark.org.tr/en/download/article-file/3158438prey-predatormodelfractional orderbifurcationsmaximum lyapunovexponentsfractal dimensionschaos control |
| spellingShingle | G.s. Mahapatra Sarker Md Sohel Rana Md. Jasim Uddin P. K. Santra Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response Chaos Theory and Applications prey-predatormodel fractional order bifurcations maximum lyapunovexponents fractal dimensions chaos control |
| title | Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response |
| title_full | Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response |
| title_fullStr | Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response |
| title_full_unstemmed | Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response |
| title_short | Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response |
| title_sort | chaotic dynamics of the fractional order predator prey model incorporating gompertz growth on prey with ivlev functional response |
| topic | prey-predatormodel fractional order bifurcations maximum lyapunovexponents fractal dimensions chaos control |
| url | https://dergipark.org.tr/en/download/article-file/3158438 |
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