论文标题
三组分反应扩散系统中带有振荡尾巴的N点环的动力学
Dynamics of N-spot rings with oscillatory tails in a three-component reaction-diffusion system
论文作者
论文摘要
在二维空间中，我们研究了在特定的三组分反应 - 扩散系统中具有振荡尾部的多个局部斑点的缓慢动力学，其关键特征是该点根据它们的相互距离或相互距离吸引或排斥，从而导致相当复杂的模式。一种基本模式是环形图案，由$ n $均等的斑点组成，上面有一定半径。根据系统的参数，可以观察到固定或移动的参数（即行进和旋转）$ n $ -Spot环。为了了解这些模式的出现，我们通过编码每个点位置和速度的信息的一组简化的普通微分方程（ODE）来描述$ n $点的动态。根据减少的系统，我们分析研究了固定和移动$ n $ spot环溶液的存在和稳定性，类似于自propelled颗粒的集体运动。提供数值模拟以用固定参数验证我们的结果。
In two-dimensional space, we investigate the slow dynamics of multiple localized spots with oscillatory tails in a specific three-component reaction-diffusion system, whose key feature is that the spots attract or repel each other alternatively according to their mutual distances, leading to rather complex patterns. One fundamental pattern is the ring pattern, consisting of $N$ equally distributed spots on a circle with a certain radius. Depending on the parameters of the system, stationary or moving (i.e., traveling and rotating) $N$-spot rings can be observed. In order to understand the emergence of these patterns, we describe the dynamics of $N$ spots by a set of reduced ordinary differential equations (ODEs) encoding the information of each spot's location and velocity. On the basis of the reduced system, we analytically study the existence and stability of stationary and moving $N$-spot ring solutions, similar to the collective motion of self-propelled particles. Numerical simulations are provided to verify our results with fixed parameters.
