Grindrod P, Gomatam J
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, UK.
J Math Biol. 1987;25(6):597-610. doi: 10.1007/BF00275496.
Chemical or biological systems modelled by reaction diffusion (R.D.) equations which support simple one-dimensional travelling waves (oscillatory or otherwise) may be expected to produce intricate two- or three-dimensional spatial patterns, either stationary or subject to certain motion. Such structures have been observed experimentally. Asymptotic considerations applied to a general class of such systems lead to fundamental restrictions on the existence and geometrical form of possible structures. As a consequence of the geometrical setting, it is a straightforward matter to consider the propagation of waves on closed two-dimensional manifolds. We derive a fundamental equation for R.D. wave propagation on surfaces and discuss its significance. We consider the existence and propagation of rotationally symmetric and double spiral waves on the sphere and on the torus.
由反应扩散（R.D.）方程建模的化学或生物系统，若能支持简单的一维行波（振荡或其他形式），则有望产生复杂的二维或三维空间模式，这些模式可以是静态的，也可以是受特定运动影响的。此类结构已通过实验观测到。对这类一般系统应用渐近分析会对可能结构的存在性和几何形式产生基本限制。由于几何设定，考虑波在封闭二维流形上的传播是一件直接的事情。我们推导了表面上R.D.波传播的基本方程并讨论其意义。我们考虑球面上和环面上旋转对称波和双螺旋波的存在与传播。
