Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure
Abstract Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation on the pattern formation of a discre...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2328-5 |
| _version_ | 1811322301716627456 |
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| author | Tousheng Huang Huayong Zhang Zhengran Hu Ge Pan Shengnan Ma Xiumin Zhang Zichun Gao |
| author_facet | Tousheng Huang Huayong Zhang Zhengran Hu Ge Pan Shengnan Ma Xiumin Zhang Zichun Gao |
| author_sort | Tousheng Huang |
| collection | DOAJ |
| description | Abstract Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation on the pattern formation of a discrete predator–prey system where the population diffusion is based on the Moore neighborhood structure instead of the von Neumann neighborhood structure widely applied previously. Under pattern formation conditions which are determined by Turing instability analysis, numerical simulations are performed to reveal the spatiotemporal complexity of the system. A pure Turing instability can induce the self-organization of many basic types of patterns as described in the literature, as well as new spiral-spot and labyrinth patterns which show the temporally oscillating and chaotic property. Neimark–Sacker–Turing and flip–Turing instability can lead to the formation of circle, spiral and much more complex patterns, which are self-organized via spatial symmetry breaking on the states that are homogeneous in space and non-periodic in time. Especially, the emergence of spiral pattern suggests that spatial order can generate from temporal disorder, implying that even when the predator–prey dynamics in one site is chaotic, the spatially global dynamics may still be predictable. The results obtained in this research suggest that when the way of population diffusion changes, the pattern formation in the predator–prey systems demonstrates great differences. This may provide realistic significance to explain more general predator–prey coexistence. |
| first_indexed | 2024-04-13T13:32:46Z |
| format | Article |
| id | doaj.art-8d073f71aaac456496d0ec9cdd62fe8e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T13:32:46Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-8d073f71aaac456496d0ec9cdd62fe8e2022-12-22T02:44:53ZengSpringerOpenAdvances in Difference Equations1687-18472019-09-012019112010.1186/s13662-019-2328-5Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structureTousheng Huang0Huayong Zhang1Zhengran Hu2Ge Pan3Shengnan Ma4Xiumin Zhang5Zichun Gao6Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power UniversityAbstract Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation on the pattern formation of a discrete predator–prey system where the population diffusion is based on the Moore neighborhood structure instead of the von Neumann neighborhood structure widely applied previously. Under pattern formation conditions which are determined by Turing instability analysis, numerical simulations are performed to reveal the spatiotemporal complexity of the system. A pure Turing instability can induce the self-organization of many basic types of patterns as described in the literature, as well as new spiral-spot and labyrinth patterns which show the temporally oscillating and chaotic property. Neimark–Sacker–Turing and flip–Turing instability can lead to the formation of circle, spiral and much more complex patterns, which are self-organized via spatial symmetry breaking on the states that are homogeneous in space and non-periodic in time. Especially, the emergence of spiral pattern suggests that spatial order can generate from temporal disorder, implying that even when the predator–prey dynamics in one site is chaotic, the spatially global dynamics may still be predictable. The results obtained in this research suggest that when the way of population diffusion changes, the pattern formation in the predator–prey systems demonstrates great differences. This may provide realistic significance to explain more general predator–prey coexistence.http://link.springer.com/article/10.1186/s13662-019-2328-5Discrete predator–prey systemMoore neighborhood structurePattern formationSpatiotemporal dynamicsCoupled map lattice |
| spellingShingle | Tousheng Huang Huayong Zhang Zhengran Hu Ge Pan Shengnan Ma Xiumin Zhang Zichun Gao Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure Advances in Difference Equations Discrete predator–prey system Moore neighborhood structure Pattern formation Spatiotemporal dynamics Coupled map lattice |
| title | Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure |
| title_full | Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure |
| title_fullStr | Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure |
| title_full_unstemmed | Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure |
| title_short | Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure |
| title_sort | predator prey pattern formation driven by population diffusion based on moore neighborhood structure |
| topic | Discrete predator–prey system Moore neighborhood structure Pattern formation Spatiotemporal dynamics Coupled map lattice |
| url | http://link.springer.com/article/10.1186/s13662-019-2328-5 |
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