Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model
In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis. Then, we show that the discrete model has the flip b...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/9592878 |
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| _version_ | 1832558775948541952 |
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| author | Lili Meng Yutao Han Zhiyi Lu Guang Zhang |
| author_facet | Lili Meng Yutao Han Zhiyi Lu Guang Zhang |
| author_sort | Lili Meng |
| collection | DOAJ |
| description | In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis. Then, we show that the discrete model has the flip bifurcation and Turing bifurcation under the critical parameter values. Finally, a series of numerical simulations are carried out in the Turing instability region of the discrete predator-prey model; some new Turing patterns such as striped, bar, and horizontal bar are observed. |
| format | Article |
| id | doaj-art-122430202703457e9d7d70d9c3bc084c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-122430202703457e9d7d70d9c3bc084c2025-02-03T01:31:32ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/95928789592878Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion ModelLili Meng0Yutao Han1Zhiyi Lu2Guang Zhang3School of Science, Tianjin University of Commerce, Tianjin 300134, ChinaDepartment of Economics, University of International Business and Economics, Beijing 100029, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaIn this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis. Then, we show that the discrete model has the flip bifurcation and Turing bifurcation under the critical parameter values. Finally, a series of numerical simulations are carried out in the Turing instability region of the discrete predator-prey model; some new Turing patterns such as striped, bar, and horizontal bar are observed.http://dx.doi.org/10.1155/2019/9592878 |
| spellingShingle | Lili Meng Yutao Han Zhiyi Lu Guang Zhang Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model Discrete Dynamics in Nature and Society |
| title | Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model |
| title_full | Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model |
| title_fullStr | Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model |
| title_full_unstemmed | Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model |
| title_short | Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model |
| title_sort | bifurcation chaos and pattern formation for the discrete predator prey reaction diffusion model |
| url | http://dx.doi.org/10.1155/2019/9592878 |
| work_keys_str_mv | AT lilimeng bifurcationchaosandpatternformationforthediscretepredatorpreyreactiondiffusionmodel AT yutaohan bifurcationchaosandpatternformationforthediscretepredatorpreyreactiondiffusionmodel AT zhiyilu bifurcationchaosandpatternformationforthediscretepredatorpreyreactiondiffusionmodel AT guangzhang bifurcationchaosandpatternformationforthediscretepredatorpreyreactiondiffusionmodel |