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)
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
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.
Received: 04 April 2008
Revised: 22 September 2008
Accepted manuscript online:
PACS:
87.23.Cc
(Population dynamics and ecological pattern formation)
Fund: 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),
Cite this article:
Liu Quan-Xing(刘权兴), Sun Gui-Quan(孙桂全), Jin Zhen(靳祯), and Li Bai-Lian(李百炼) Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems 2009 Chin. Phys. B 18 506
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