非对称非局部耦合控制的反应扩散型动力学作为微分平流的极限情形
Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as limiting case of differential advection
摘要：
作为微分平流两组分活化剂-抑制剂反应扩散模型的极限情形，导出了一个具有非对称非局部耦合的单组分扩散反应扩散系统.在这样一个反应扩散系统中的非对称非局部耦合的影响，然后与以前研究的对称非局部耦合系统的情况进行比较。我们对模型的空间均匀定态进行了线性稳定性分析，并对模型进行了数值模拟，以显示非对称非局部耦合如何控制和改变系统的定态和前沿动态。在第二步中，包括第三快速反应扩散方程，其导致形成更复杂的图案。线性稳定性分析预测行波的非对称非局部耦合的静态图灵模式与对称非局部耦合的系统。这些发现是通过直接数值积分的完整方程与非局部耦合验证。
英文摘要：
A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusi on system are then compared to the previously studied case of a system with symm etric nonlocal coupling. We carry out a linear stability analysis of the spatially homogeneous steady sta tes of the model and numerical simulations of the model to show how the asymmetr ic nonlocal coupling controls and alters the steady states and the front dynamic s in the system. In a second step, a third fast reaction-diffusion equation is included which ind uces the formation of more complex patterns. A linear stability analysis predicts traveling waves for asymmetric nonlocal coupling in contrast to a stationary Turing patterns for a system with symmetric nonlocal coupling. These findings are verified by direct numerical integration of the full equations with nonlocal coupling.
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