Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems |
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Authors: | Liu Quan-Xing Sun Gui-Quan Jin Zhen and Li Bai-Lian |
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Institution: | Department of Mathematics, North University of China, Taiyuan, 030051, China; Ecological Complexity and Modeling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside, CA 92521-0124, USA |
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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. |
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Keywords: | reaction--diffusion systems travelling wave bifurcation |
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