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A new finding on pattern self-organization along the route to chaos

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  • Zhang, Huayong
  • Ma, Shengnan
  • Huang, Tousheng
  • Cong, Xuebing
  • Yang, Hongju
  • Zhang, Feifan

Abstract

This research investigates pattern self-organization along the route to chaos in a space- and time-discrete predator–prey system, where the prey shows convection movement in space. Through analysis on Turing instability of the system, pattern self-organization conditions are determined. Based on the conditions, simulations are performed under two initial conditions, demonstrating two pattern transitions along the route to chaos. In the first pattern transition, the patterns start from regular stripes, experiencing twisted stripes, then return to regular stripes again. The second pattern transition is much more complex and shows three stages. Especially, an alternation between ordered patterns and disordered chaos is found, contributing greatly to the spatiotemporal complexity of the system. When the system stays at the homogeneous chaotic states, Turing instability driven by convection and diffusion can still force the self-organization of regular striped patterns. The finding in this research provides a new comprehending for pattern self-organization and transition in spatially extended predator–prey systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:118-130
    DOI: 10.1016/j.chaos.2017.11.016
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    References listed on IDEAS

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    1. Abid, Walid & Yafia, Radouane & Aziz-Alaoui, M.A. & Bouhafa, Habib & Abichou, Azgal, 2015. "Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 292-313.
    2. Wang, Caiyun, 2015. "Rich dynamics of a predator–prey model with spatial motion," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 1-9.
    3. Yongli Cai & Caidi Zhao & Weiming Wang, 2013. "Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-16, December.
    4. Schreiber, Sebastian J. & Killingback, Timothy P., 2013. "Spatial heterogeneity promotes coexistence of rock–paper–scissors metacommunities," Theoretical Population Biology, Elsevier, vol. 86(C), pages 1-11.
    5. 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.
    6. Chang, Lili & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen, 2015. "Rich dynamics in a spatial predator–prey model with delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 540-550.
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    Cited by:

    1. 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.
    2. Zhang, Huayong & Guo, Fenglu & Zou, Hengchao & Zhao, Lei & Wang, Zhongyu & Yuan, Xiaotong & Liu, Zhao, 2024. "Refuge-driven spatiotemporal chaos in a discrete predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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