Solving a system of nonlinear difference equations with bilinear dynamics
This paper presented a comprehensive study of a three-dimensional nonlinear system of difference equations, which can be reduced to a two-dimensional bilinear system. The system monitored the evolution of three sequences $ \left(P_{m}\right), $ $ \left(Q_{m}\right), $ $ \left(R_{m}\right) $, gover...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241624 |
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| author | Hashem Althagafi Ahmed Ghezal |
| author_facet | Hashem Althagafi Ahmed Ghezal |
| author_sort | Hashem Althagafi |
| collection | DOAJ |
| description | This paper presented a comprehensive study of a three-dimensional nonlinear system of difference equations, which can be reduced to a two-dimensional bilinear system. The system monitored the evolution of three sequences $ \left(P_{m}\right), $ $ \left(Q_{m}\right), $ $ \left(R_{m}\right) $, governed by recursive relations. We investigated the solvability of this system and provided general closed-form solutions for various parameter conditions. Furthermore, the simulations provided valuable insights into the dynamic behavior of animals, modeled using recursive difference equations. The model encapsulated essential behavioral metrics, represented by the variables $ P $, $ Q $, and $ R $, which corresponded to individual actions, social interactions, and environmental stressors, respectively. These variables adapted dynamically in response to internal and external influences, illustrating the system's sensitivity to various behavioral and environmental conditions. |
| format | Article |
| id | doaj-art-23f9201a1b154f8085d2475581f08cda |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-23f9201a1b154f8085d2475581f08cda2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912340673408910.3934/math.20241624Solving a system of nonlinear difference equations with bilinear dynamicsHashem Althagafi0Ahmed Ghezal1Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi ArabiaDepartment of Mathematics, Abdelhafid Boussouf University Center of Mila, AlgeriaThis paper presented a comprehensive study of a three-dimensional nonlinear system of difference equations, which can be reduced to a two-dimensional bilinear system. The system monitored the evolution of three sequences $ \left(P_{m}\right), $ $ \left(Q_{m}\right), $ $ \left(R_{m}\right) $, governed by recursive relations. We investigated the solvability of this system and provided general closed-form solutions for various parameter conditions. Furthermore, the simulations provided valuable insights into the dynamic behavior of animals, modeled using recursive difference equations. The model encapsulated essential behavioral metrics, represented by the variables $ P $, $ Q $, and $ R $, which corresponded to individual actions, social interactions, and environmental stressors, respectively. These variables adapted dynamically in response to internal and external influences, illustrating the system's sensitivity to various behavioral and environmental conditions.https://www.aimspress.com/article/doi/10.3934/math.20241624nonlinear difference equationsbilinear systemsclosed-form solutionsnumerical simulationsanimal behavior modelingsystem dynamics |
| spellingShingle | Hashem Althagafi Ahmed Ghezal Solving a system of nonlinear difference equations with bilinear dynamics AIMS Mathematics nonlinear difference equations bilinear systems closed-form solutions numerical simulations animal behavior modeling system dynamics |
| title | Solving a system of nonlinear difference equations with bilinear dynamics |
| title_full | Solving a system of nonlinear difference equations with bilinear dynamics |
| title_fullStr | Solving a system of nonlinear difference equations with bilinear dynamics |
| title_full_unstemmed | Solving a system of nonlinear difference equations with bilinear dynamics |
| title_short | Solving a system of nonlinear difference equations with bilinear dynamics |
| title_sort | solving a system of nonlinear difference equations with bilinear dynamics |
| topic | nonlinear difference equations bilinear systems closed-form solutions numerical simulations animal behavior modeling system dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241624 |
| work_keys_str_mv | AT hashemalthagafi solvingasystemofnonlineardifferenceequationswithbilineardynamics AT ahmedghezal solvingasystemofnonlineardifferenceequationswithbilineardynamics |