一类四阶系统的扩散驱动不稳定性
Diffusion-Driven Instability of a fourth order system
摘要：
我们分析了反应扩散系统的扩散驱动（图灵）不稳定性。本文的创新之处在于用四阶双拉普拉斯算子和二阶拉普拉斯算子的组合来代替传统的拉普拉斯扩散算子。当四阶项和二阶项竞争时，我们发现了新的现象，这意味着其中一个使系统稳定，而另一个使系统不稳定。我们用系统中的参数值来表征图灵空间，也用域的大小和张力参数来找到不稳定的判据。
英文摘要：
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second order Laplacian. We find new phenomena when the fourth order and second order terms are competing, meaning one of them stabilizes the system whereas the other destabilizes it. We characterize Turing space in terms of parameter values in the system, and also find criteria for instability in terms of the domain size and tension parameter.
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