中国物理B ›› 2009, Vol. 18 ›› Issue (2): 506-515.doi: 10.1088/1674-1056/18/2/021

• GENERAL • 上一篇    下一篇

Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems

刘权兴1, 孙桂全1, 靳祯1, 李百炼2   

  1. (1)Department of Mathematics, North University of China, Taiyuan, 030051, China; (2)Ecological Complexity and Modeling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside, CA 92521-0124, USA
  • 收稿日期:2008-04-04 修回日期:2008-09-22 出版日期:2009-02-20 发布日期:2009-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60771026), the Program for New Century Excellent Talents in University (Grant No NCET050271), the Natural Science Foundation of Shan'xi Province, China (Grant No 2006011009),

Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems

Liu Quan-Xing(刘权兴)a), Sun Gui-Quan(孙桂全)a), Jin Zhen(靳祯)a)†, and Li Bai-Lian(李百炼)b)   

  1. a Department of Mathematics, North University of China, Taiyuan, 030051, China; b Ecological Complexity and Modeling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside, CA 92521-0124, USA
  • Received:2008-04-04 Revised:2008-09-22 Online:2009-02-20 Published:2009-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60771026), the Program for New Century Excellent Talents in University (Grant No NCET050271), the Natural Science Foundation of Shan'xi Province, China (Grant No 2006011009),

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摘要： It has been reported that the minimal spatially extended phytoplankton--zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing--Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.

Abstract: It has been reported that the minimal spatially extended phytoplankton--zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing--Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.

Key words: reaction--diffusion systems, travelling wave, bifurcation

中图分类号:  (Population dynamics and ecological pattern formation)

  • 87.23.Cc
87.23.Kg (Dynamics of evolution) 05.45.-a (Nonlinear dynamics and chaos) 05.60.-k (Transport processes)