Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator
We apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top preda...
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1702 |
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| author | Ajay Kumar Sara Salem Alzaid Badr Saad T. Alkahtani Sunil Kumar |
| author_facet | Ajay Kumar Sara Salem Alzaid Badr Saad T. Alkahtani Sunil Kumar |
| author_sort | Ajay Kumar |
| collection | DOAJ |
| description | We apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top predators, and the top predators are also divided into mature and immature predators. We calculated the uniqueness and existence of the solutions applying the fixed-point hypothesis. Our study examines the possibility of obtaining new dynamical phase portraits with the new generalized Caputo operator and demonstrates the portraits for several values of fractional order. A generalized predictor–corrector (P-C) approach is utilized in numerically solving this food web model. In the case of the nonlinear equations system, the effectiveness of the used scheme is highly evident and easy to implement. In addition, stability analysis was conducted for this numerical scheme. |
| first_indexed | 2024-03-10T03:29:06Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:29:06Z |
| publishDate | 2022-05-01 |
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| spelling | doaj.art-913773f325164b099322dc99dcc0fcbc2023-11-23T12:01:09ZengMDPI AGMathematics2227-73902022-05-011010170210.3390/math10101702Complex Dynamic Behaviour of Food Web Model with Generalized Fractional OperatorAjay Kumar0Sara Salem Alzaid1Badr Saad T. Alkahtani2Sunil Kumar3Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, IndiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi ArabiaDepartment of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, IndiaWe apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top predators, and the top predators are also divided into mature and immature predators. We calculated the uniqueness and existence of the solutions applying the fixed-point hypothesis. Our study examines the possibility of obtaining new dynamical phase portraits with the new generalized Caputo operator and demonstrates the portraits for several values of fractional order. A generalized predictor–corrector (P-C) approach is utilized in numerically solving this food web model. In the case of the nonlinear equations system, the effectiveness of the used scheme is highly evident and easy to implement. In addition, stability analysis was conducted for this numerical scheme.https://www.mdpi.com/2227-7390/10/10/1702food web model (FWM)dynamical behaviourgeneralized Caputo operatoruniquenessstabilityexistence |
| spellingShingle | Ajay Kumar Sara Salem Alzaid Badr Saad T. Alkahtani Sunil Kumar Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator Mathematics food web model (FWM) dynamical behaviour generalized Caputo operator uniqueness stability existence |
| title | Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator |
| title_full | Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator |
| title_fullStr | Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator |
| title_full_unstemmed | Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator |
| title_short | Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator |
| title_sort | complex dynamic behaviour of food web model with generalized fractional operator |
| topic | food web model (FWM) dynamical behaviour generalized Caputo operator uniqueness stability existence |
| url | https://www.mdpi.com/2227-7390/10/10/1702 |
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