Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges
This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are comp...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2024/9185585 |
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| _version_ | 1832553231960506368 |
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| author | Wei Li Chunrui Zhang Mi Wang |
| author_facet | Wei Li Chunrui Zhang Mi Wang |
| author_sort | Wei Li |
| collection | DOAJ |
| description | This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model. |
| format | Article |
| id | doaj-art-f20ab5eb265248b4bda2205021092607 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f20ab5eb265248b4bda22050210926072025-02-03T05:54:44ZengWileyDiscrete Dynamics in Nature and Society1607-887X2024-01-01202410.1155/2024/9185585Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and RefugesWei Li0Chunrui Zhang1Mi Wang2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.http://dx.doi.org/10.1155/2024/9185585 |
| spellingShingle | Wei Li Chunrui Zhang Mi Wang Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges Discrete Dynamics in Nature and Society |
| title | Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges |
| title_full | Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges |
| title_fullStr | Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges |
| title_full_unstemmed | Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges |
| title_short | Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges |
| title_sort | analysis of the dynamical properties of discrete predator prey systems with fear effects and refuges |
| url | http://dx.doi.org/10.1155/2024/9185585 |
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