一类反应扩散系统的球对称模式(Ⅰ)

Spherically Symmetric Patterns for a Class of Reaction-Diffusion Systems

应用分岔理论对在一类反应扩散系统中所出现的定态空间模式进行了详细的研究,在固定边界条件下导出了其球对称模式的解析表达式,并对其进行了稳定性分析。结果表明,球的半径存在着一个上临界值,当球的半径小于上临界值时,就能从均匀分布状态自发地形成空间模式,且该模式在扩散系数的一定取值范围内是稳定的。

The steady state spatial patterns arising in a class of reaction-diffusion systems are studied by applying bifurcation theory, and analytical expressions for spherically symmetric patterns under the fixed boundary condition is derived. The results show that there exists an upper critical radius of the sphere, when the radius is less than the critical volue, a spatial pattern may arise spontaneously from a uniform distribution. However, the spatial patterns exist only in a certain range of values of the diffusion coefficients.