Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system
Abstract A spatiotemporal discrete predator–prey system is investigated for understanding the pattern self-organization on the route to chaos. The discrete system is modelled by a coupled map lattice and shows advection of populations in space. Based on the conditions of stable stationary states and...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1598-7 |
| _version_ | 1811225380166565888 |
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| author | Tousheng Huang Xuebing Cong Huayong Zhang Shengnan Ma Ge Pan |
| author_facet | Tousheng Huang Xuebing Cong Huayong Zhang Shengnan Ma Ge Pan |
| author_sort | Tousheng Huang |
| collection | DOAJ |
| description | Abstract A spatiotemporal discrete predator–prey system is investigated for understanding the pattern self-organization on the route to chaos. The discrete system is modelled by a coupled map lattice and shows advection of populations in space. Based on the conditions of stable stationary states and Hopf bifurcation, Turing pattern formation conditions are determined. As the parameter value is changed, self-organization of diverse patterns and complex phase transition among the patterns on the route to chaos are observed in simulations. Ordered patterns of stripes, bands, circles, and various disordered states are revealed. When we zoom in to observe the pattern transition in smaller and smaller parameter ranges, subtle structures for transition process are found: (1) alternation between self-organized structured patterns and disordered states emerges as the main nonlinear characteristic; (2) when the parameter value varies in the level from 10−3 to 10−4, a cyclic pattern transition process occurs repeatedly; (3) when the parameter value shifts in the level of 10−5 or below, stochastic pattern fluctuation dominates as essential regularity for pattern variations. The results obtained in this research promote comprehending pattern self-organization and pattern transition on the route to chaos in spatiotemporal predator–prey systems. |
| first_indexed | 2024-04-12T09:06:19Z |
| format | Article |
| id | doaj.art-a9e160a4b8a941f0bd32a32c82aed3df |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-12T09:06:19Z |
| publishDate | 2018-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-a9e160a4b8a941f0bd32a32c82aed3df2022-12-22T03:39:06ZengSpringerOpenAdvances in Difference Equations1687-18472018-05-012018112110.1186/s13662-018-1598-7Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey systemTousheng Huang0Xuebing Cong1Huayong Zhang2Shengnan Ma3Ge Pan4Research 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 A spatiotemporal discrete predator–prey system is investigated for understanding the pattern self-organization on the route to chaos. The discrete system is modelled by a coupled map lattice and shows advection of populations in space. Based on the conditions of stable stationary states and Hopf bifurcation, Turing pattern formation conditions are determined. As the parameter value is changed, self-organization of diverse patterns and complex phase transition among the patterns on the route to chaos are observed in simulations. Ordered patterns of stripes, bands, circles, and various disordered states are revealed. When we zoom in to observe the pattern transition in smaller and smaller parameter ranges, subtle structures for transition process are found: (1) alternation between self-organized structured patterns and disordered states emerges as the main nonlinear characteristic; (2) when the parameter value varies in the level from 10−3 to 10−4, a cyclic pattern transition process occurs repeatedly; (3) when the parameter value shifts in the level of 10−5 or below, stochastic pattern fluctuation dominates as essential regularity for pattern variations. The results obtained in this research promote comprehending pattern self-organization and pattern transition on the route to chaos in spatiotemporal predator–prey systems.http://link.springer.com/article/10.1186/s13662-018-1598-7Self-organizationChaosCoupled map latticeBifurcationTuring instabilityPredator–prey system |
| spellingShingle | Tousheng Huang Xuebing Cong Huayong Zhang Shengnan Ma Ge Pan Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system Advances in Difference Equations Self-organization Chaos Coupled map lattice Bifurcation Turing instability Predator–prey system |
| title | Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system |
| title_full | Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system |
| title_fullStr | Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system |
| title_full_unstemmed | Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system |
| title_short | Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator–prey system |
| title_sort | pattern self organization and pattern transition on the route to chaos in a spatiotemporal discrete predator prey system |
| topic | Self-organization Chaos Coupled map lattice Bifurcation Turing instability Predator–prey system |
| url | http://link.springer.com/article/10.1186/s13662-018-1598-7 |
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