Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure
| Autor: | Huayong Zhang, Shengnan Ma, Ge Pan, Zichun Gao, Xiumin Zhang, Zhengran Hu, Tousheng Huang |
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| Rok vydání: | 2019 |
| Předmět: |
0106 biological sciences
Population Coupled map lattice Chaotic Pattern formation 010603 evolutionary biology 01 natural sciences Instability Von Neumann neighborhood Spatiotemporal dynamics 0103 physical sciences Discrete predator–prey system Quantitative Biology::Populations and Evolution Statistical physics Symmetry breaking education 010301 acoustics Mathematics education.field_of_study Algebra and Number Theory lcsh:Mathematics Applied Mathematics lcsh:QA1-939 Moore neighborhood Moore neighborhood structure Analysis |
| Zdroj: | Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-20 (2019) |
| ISSN: | 1687-1847 |
| DOI: | 10.1186/s13662-019-2328-5 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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