浮游生物生态系统中螺旋波远场分裂驱动的时空混沌
Emergence of spatiotemporal chaos driven by far-field breakup of spiral waves in the plankton ecological systems
摘要：
亚历山大湾Medvinsky \emph{et al} [A. B.梅德文斯基岛A.吉洪诺娃河R.阿利耶夫湾L.李志S. Lin和H. Malchow，Phys. Rev. \textbf{64}，021915（2001）]和Marcus R. Garvie \emph{et al} [M. R. Garvie和C. Trenchea，SIAM J。控制。Optim。\textbf{46}，775-791（2007）]表明，浮游植物-浮游动物的最小空间扩展反应扩散模型可以在斑块环境中表现出规则的、混沌的行为和时空模式。在此基础上，本文通过计算机模拟和理论分析，进一步研究了空间浮游生物模型在混合Turing-Hopf分岔区域下的参数期望值。研究结果表明，在浮游植物和浮游动物扩散系数较大的范围内，螺旋波在该区域存在，时空混沌出现，这是由于螺旋波的远场分裂引起的。此外，由螺旋波远场分裂引起的时空混沌并不逐渐涉及该区域内的整个空间。计算谱和波列的非线性分叉证实了我们的结果。最后，我们从群落水平上对空间结构模式进行了解释。
英文摘要：
Alexander B. Medvinsky \emph{et al} [A. B. Medvinsky, I. A. Tikhonova, R. R. Aliev, B.-L. Li, Z.-S. Lin, and H. Malchow, Phys. Rev. E \textbf{64}, 021915 (2001)] and Marcus R. Garvie \emph{et al} [M. R. Garvie and C. Trenchea, SIAM J. Control. Optim. \textbf{46}, 775-791 (2007)] shown that the minimal spatially extended reaction-diffusion model of phytoplankton-zooplankton can exhibit both regular, chaotic behavior, and spatiotemporal patterns in a patchy environment. Based on that, the spatial plankton model is furtherly investigated by means of computer simulations and theoretical analysis in the present paper when its parameters would be expected in the case of mixed Turing-Hopf bifurcation region. Our results show that the spiral waves exist in that region and the spatiotemporal chaos emerge, which arise from the far-field breakup of the spiral waves over large ranges of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually involve the whole space within that region. Our results are confirmed by means of computation spectra and nonlinear bifurcation of wave trains. Finally, we give some explanations about the spatially structured patterns from the community level.
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