Shitara K, Hiraiwa T, Ohta T
Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066208. doi: 10.1103/PhysRevE.83.066208. Epub 2011 Jun 21.
We derive a set of equations of motion for an isolated domain in an excitable reaction-diffusion system in three dimensions. In the singular limit where the interface is infinitesimally thin, the motion of the center of mass coupled with deformation is investigated near the drift bifurcation where a motionless domain becomes unstable and undergoes migration. This is an extension of our previous theory in two dimensions. We show that there are three basic motions of a domain, straight motion, rotating motion, and helical motion. The last one is a characteristic of three dimensions. The phase diagram of these three solutions is given in the parameter space of the original reaction-diffusion equations.
我们推导了三维可激发反应扩散系统中孤立区域的一组运动方程。在界面无限薄的奇异极限下，研究了质心运动与变形耦合的情况，该情况发生在静止区域变得不稳定并开始迁移的漂移分岔附近。这是我们之前二维理论的扩展。我们表明，区域存在三种基本运动：直线运动、旋转运动和螺旋运动。最后一种是三维的特征。这三种解的相图在原始反应扩散方程的参数空间中给出。
