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Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice

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  • Tousheng Huang
  • Huayong Zhang
  • Xuebing Cong
  • Ge Pan
  • Xiumin Zhang
  • Zhao Liu

Abstract

The topic of utilizing coupled map lattice to investigate complex spatiotemporal dynamics has attracted a lot of interest. For exploring the spatiotemporal complexity of a predator-prey system with migration and diffusion, a new three-chain coupled map lattice model is developed in this research. Based on Turing instability analysis, pattern formation conditions for the predator-prey system are derived. Via numerical simulation, rich Turing patterns are found with subtle self-organized structures under diffusion-driven and migration-driven mechanisms. With the variation of migration rates, the predator-prey system exhibits a gradual dynamical transition from diffusion-driven patterns to migration-driven patterns. Moreover, new results, the self-organization of non-Turing patterns, are also revealed. We find that even in the cases where the nonspatial predator-prey system reaches collapse, the migration can still drive pattern self-organization. These non-Turing patterns suggest many new possible ways for the coexistence of predator and prey in space, under the effects of migration and diffusion.

Suggested Citation

  • Tousheng Huang & Huayong Zhang & Xuebing Cong & Ge Pan & Xiumin Zhang & Zhao Liu, 2019. "Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice," Complexity, Hindawi, vol. 2019, pages 1-19, May.
    • Handle: RePEc:hin:complx:3148323
    DOI: 10.1155/2019/3148323
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    References listed on IDEAS

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    1. Sun, Gui-Quan & Jin, Zhen & Liu, Quan-Xing & Li, Li, 2008. "Dynamical complexity of a spatial predator–prey model with migration," Ecological Modelling, Elsevier, vol. 219(1), pages 248-255.
    2. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    3. Zhang, Huayong & Ma, Shengnan & Huang, Tousheng & Cong, Xuebing & Yang, Hongju & Zhang, Feifan, 2018. "A new finding on pattern self-organization along the route to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 118-130.
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    Cited by:

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    2. Kumar, Vikas & Kumari, Nitu, 2021. "Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Fasma Diele & Carmela Marangi, 2019. "Geometric Numerical Integration in Ecological Modelling," Mathematics, MDPI, vol. 8(1), pages 1-30, December.

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