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Dynamical complexity of a spatial predator–prey model with migration

Author

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  • Sun, Gui-Quan
  • Jin, Zhen
  • Liu, Quan-Xing
  • Li, Li

Abstract

Spatial component of ecological interactions has been identified as an important factor in how ecological communities are shaped. Thus, in this paper, spatial pattern of a spatial predator–prey model, which is combined with migration and diffusion, is investigated. We present the emergence of spatial pattern by both theoretical analysis and numerical simulations. Our study reveals that migration has great influence on the pattern formation. More specifically, travelling pattern can be induced by it. Furthermore, wavelength of the travelling pattern with respect to the diffusion coefficient of the predator is calculated. The obtained results show that the modeling by both migration and diffusion is useful for studying the dynamic complexity of ecosystems, which well extend the finding of pattern formation in the ecosystems and may well explain the field observed in some areas.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecomod:v:219:y:2008:i:1:p:248-255
    DOI: 10.1016/j.ecolmodel.2008.08.009
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    Citations

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    Cited by:

    1. Wu, Xingjie & Huang, Wentao, 2009. "Dynamic analysis of a one-prey multi-predator impulsive system with Ivlev-type functional," Ecological Modelling, Elsevier, vol. 220(6), pages 774-783.
    2. Fasani, Stefano & Rinaldi, Sergio, 2011. "Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems," Ecological Modelling, Elsevier, vol. 222(18), pages 3449-3452.
    3. Marick, Sounov & Bhattacharya, Santanu & Bairagi, Nandadulal, 2023. "Dynamic properties of a reaction–diffusion predator–prey model with nonlinear harvesting: A linear and weakly nonlinear analysis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Zeyan Wu & Wenxiong Lin & Bailian Li & Linkun Wu & Changxun Fang & Zhixing Zhang, 2015. "Terminal Restriction Fragment Length Polymorphism Analysis of Soil Bacterial Communities under Different Vegetation Types in Subtropical Area," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-10, June.
    5. 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.
    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.
    7. Xibo Wang & Jianping Ge & Wendong Wei & Hanshi Li & Chen Wu & Ge Zhu, 2016. "Spatial Dynamics of the Communities and the Role of Major Countries in the International Rare Earths Trade: A Complex Network Analysis," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-22, May.
    8. Wang, Caiyun & Qi, Suying, 2018. "Spatial dynamics of a predator-prey system with cross diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 55-60.
    9. Wang, Caiyun, 2015. "Rich dynamics of a predator–prey model with spatial motion," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 1-9.
    10. Xiongxiong Du & Xiaoling Han & Ceyu Lei, 2022. "Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    11. Dhar, Joydip & Singh, Harkaran & Bhatti, Harbax Singh, 2015. "Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 324-335.

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