Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios
The Basener and Ross mathematical model is widely recognized for its ability to characterize the interaction between the population dynamics and resource utilization of Easter Island. In this study, we develop and investigate a discrete-time version of the Basener and Ross model. First, the existenc...
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2025-01-01
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| author | A. A. Elsadany A. M. Yousef S. A. Ghazwani A. S. Zaki |
| author_facet | A. A. Elsadany A. M. Yousef S. A. Ghazwani A. S. Zaki |
| author_sort | A. A. Elsadany |
| collection | DOAJ |
| description | The Basener and Ross mathematical model is widely recognized for its ability to characterize the interaction between the population dynamics and resource utilization of Easter Island. In this study, we develop and investigate a discrete-time version of the Basener and Ross model. First, the existence and the stability of fixed points for the present model are investigated. Next, we investigated various bifurcation scenarios by establishing criteria for the occurrence of different types of codimension-one bifurcations, including flip and Neimark–Sacker bifurcations. These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model’s complex dynamical structure. Numerical simulations are employed to validate and illustrate the theoretical predictions. Finally, through bifurcation diagrams, maximal Lyapunov exponents, and phase portraits, we uncover a diversity of dynamical characteristics, including limit cycles, periodic solutions, and chaotic attractors. |
| format | Article |
| id | doaj-art-be1401e358004f2884197c54270bf576 |
| institution | Kabale University |
| issn | 2079-3197 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj-art-be1401e358004f2884197c54270bf5762025-01-24T13:27:47ZengMDPI AGComputation2079-31972025-01-011311110.3390/computation13010011Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple ScenariosA. A. Elsadany0A. M. Yousef1S. A. Ghazwani2A. S. Zaki3Mathematics Department, College of Science and Humanities Studies in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaMathematics Department, Faculty of Science, South Valley University, Qena 83523, EgyptMathematics Department, College of Science and Humanities Studies in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaMathematics Department, Faculty of Science, Aswan University, Aswan 81528, EgyptThe Basener and Ross mathematical model is widely recognized for its ability to characterize the interaction between the population dynamics and resource utilization of Easter Island. In this study, we develop and investigate a discrete-time version of the Basener and Ross model. First, the existence and the stability of fixed points for the present model are investigated. Next, we investigated various bifurcation scenarios by establishing criteria for the occurrence of different types of codimension-one bifurcations, including flip and Neimark–Sacker bifurcations. These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model’s complex dynamical structure. Numerical simulations are employed to validate and illustrate the theoretical predictions. Finally, through bifurcation diagrams, maximal Lyapunov exponents, and phase portraits, we uncover a diversity of dynamical characteristics, including limit cycles, periodic solutions, and chaotic attractors.https://www.mdpi.com/2079-3197/13/1/11population model dynamicsstability analysiscodimension-one bifurcationcodimension-two bifurcation |
| spellingShingle | A. A. Elsadany A. M. Yousef S. A. Ghazwani A. S. Zaki Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios Computation population model dynamics stability analysis codimension-one bifurcation codimension-two bifurcation |
| title | Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios |
| title_full | Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios |
| title_fullStr | Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios |
| title_full_unstemmed | Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios |
| title_short | Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios |
| title_sort | bifurcation analysis of a discrete basener ross population model exploring multiple scenarios |
| topic | population model dynamics stability analysis codimension-one bifurcation codimension-two bifurcation |
| url | https://www.mdpi.com/2079-3197/13/1/11 |
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