存在对流时的极限环，行波分析
Limit cycles in the presence of convection, a travelling wave analysis
摘要：
考虑了一类具有极限环反应函数的扩散模型。我们选择了一组功能来自一个现实的反应模型：Schnakenberg方程。这种合成形式是不对称的。我们找到一个变换，映射到模型形式的不规则方程。接下来，我们将因变量转换为极坐标形式。从这里开始，对径向变量进行行波分析。结果是复杂的，但我们做了一些简单的估计。我们进行了数值实验来验证我们的分析。初始的“敲击”开始模式的传播。行波的速度与预期的不太一样。我们会进一步调查。该系统表现出明显不同的行为，以左和右。我们解释了这种现象是如何发生的，通过检查潜在的行为。
英文摘要：
We consider a diffusion model with limit cycle reaction functions, in the presence of convection. We select a set of functions derived from a realistic reaction model: the Schnakenberg equations. This resultant form is unsymmetrical. We find a transformation which maps the irregular equations into model form. Next we transform the dependent variables into polar form. From here, a travelling wave analysis is performed on the radial variable. Results are complex, but we make some simple estimates. We carry out numerical experiments to test our analysis. An initial `knock' starts the propagation of pattern. The speed of the travelling wave is not quite as expected. We investigate further. The system demonstrates distinctly different behaviour to the left and the right. We explain how this phenomenon occurs by examining the underlying behaviour.
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