论文标题
非局部相互作用引起的模式交替
Pattern alternations induced by nonlocal interactions
论文作者
论文摘要
模式形成是对复杂系统动力学的视觉理解。模式在许多方面都会出现,例如动物的分割,生长过程中的细菌菌落,植被,化学反应等。在大多数情况下,远距离扩散发生,通常的反应扩散(RD)模型无法捕获这种现象。另一方面,非本地RD模型可以填补空白。 RD系统的振幅方程(AE)的分析推导是一种有价值的工具,可以在发生时预测模式选择,特别是固定的Turing模式。在本文中,我们分析了非局部模型的图灵分叉的条件,并在图灵分叉阈值附近得出了非局部RD模型的AE,以描述模式选择背后的原因。如我们的代表性示例所示,AE的这种推导不仅限于非本地猎物预性模型,而且还可以应用于图灵分叉阈值附近的其他非局部模型。分析预测与图灵分叉阈值附近的数值模拟一致。此外,对于非局部参数的较小值,分析结果和数值结果彼此彼此更适合图灵分叉阈值,但对于较高的值而言。
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the long-range diffusion occurs, and the usual reaction-diffusion (RD) model can not capture such phenomena. The nonlocal RD model, on the other hand, can fill the gap. Analytical derivation of the amplitude equations (AE) for an RD system is a valuable tool to predict the pattern selections, in particular, the stationary Turing patterns when they occur. In this paper, we analyze the conditions for the Turing bifurcation for the nonlocal model and also derive the AE for the nonlocal RD model near the Turing bifurcation threshold to describe the reason behind the pattern selections. This derivation of the AE is not only limited to the nonlocal prey-predator model, as shown in our representative example but also can be applied to other nonlocal models near the Turing bifurcation threshold. The analytical prediction agrees with numerical simulation near the Turing bifurcation threshold. Moreover, the analytical and numerical results fit each other well even more remote from the Turing bifurcation threshold for the small values of the nonlocal parameter but not for the higher values.