反应扩散系统中时空斑图研究(英文)

Spatiotemproal pattern formation in a reaction-diffusion system

时空斑图广泛地存在于反应扩散系统中,在延展的布鲁塞尔振子模型中,一维的时空斑图已经被研究过。本文中,我们对布鲁塞尔振子模型进行线性稳定性分析,模拟出两维的时空斑图,进一步阐明斑图形成的机制,形成斑图的机制是由于霍普夫失稳、短波失稳和图灵失稳以及它们之间的相互作用。当系统处于非平衡状态下,布鲁塞尔振子模型可以得到有序的时空斑图。

Spatiotemporal pattern formations are often found in reaction-diffusion systems. One-dimension patterns have been obtained in the extended Brusselator model. In this paper, linear stability analysis is applied to the Brusselator model, a series of time-space pattern are obtained in two-dimension space by numerical simulations. Homogeneous bulk oscillations are unstable when systems are far away bifurcation point. We explain that some patterns are formed because of instabilities and interaction between instabilities. We further point out that the Brusselator model is a perfect model unraveling dissipative structure and the mechanism of patterns.