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期刊论文

Nonlinear dynamic and pattern bifurcations in a model for spatial patterns in young mussel beds

靳祯Rong-Hua Wang Quan-Xing Liu Gui-Quan Sun Zhen Jin* and Johan van de Koppel

J. R. Soc. Interface (2009) 6, 705-718,-0001,():

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摘要/描述

Young mussel beds on soft sediments can display large-scale regular spatial patterns. This phenomenon can be explained relatively simply by a reaction–diffusion–advection (RDA) model of the interaction between algae and mussel, which includes the diffusive spread of mussel and the advection of algae. We present a detailed analysis of pattern formation in this RDA model. We derived the conditions for differential-flow instability that cause the formation of spatial patterns, and then systematically investigated how these patterns depend on model parameters. We also present a detailed study of the patterned solutions in the full nonlinear model, using numerical bifurcation analysis of the ordinary differential equations, which were obtained from the RDA model. We show that spatial patterns occur for a wide range of algal concentrations, even when algal concentration is much lower than the prediction by linear analysis in the RDA model. That is to say, spatial patterns result from the interaction of nonlinear terms. Moreover, patterns with different wavelength, amplitude and movement speed may coexist. The results obtained are consistent with the previous observation that self-organization allows mussels to persist with algal concentrations that would not permit survival of mussels in a homogeneous bed.

版权说明:以下全部内容由靳祯上传于   2010年07月20日 15时19分19秒,版权归本人所有。

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