Reaction diffusion approximation of nonlocal interactions using Jacobi polynomials
Reaction diffusion approximation of nonlocal interactions using Jacobi polynomials
复制标题
使用雅可比多项式的非局部相互作用的反应扩散近似
DOI：
10.1007/s13160-017-0299-z
复制
发表时间：
2018
影响因子：
0.9
通讯作者：
Yamamoto Hiroko
中科院分区：
文献类型：
--
作者：
Ninomiya Hirokazu;Tanaka Yoshitaro;Yamamoto Hiroko
非局域相互作用是生物体的跃迁可能性、分子事件和信号网络等微观信息综合的结果，在各个领域引起了广泛的关注。非局部相互作用对于再现与这些详细的微观信息相对应的各种模式是有用的。然而，这种方法是不方便的观察目标现象背后的具体机制，因为信息的压缩。因此，我们先前提出了一种能够通过具有辅助因子的反应扩散系统来近似任何非局部相互作用的方法（二宫等人，J Math Biol 75：1203-1233，2017）。本文在适当的假设条件下，利用雅可比多项式给出了一种确定反应扩散方程组参数的显式方法。我们还介绍了一种数值方法来指定的参数的反应扩散系统的一般扩散系数的Tikhonov正则化。
Nonlocal interactions, which have attracted attention in various fields, result from the integration of microscopic information such as a transition possibility, molecular events, and signaling networks of living creatures. Nonlocal interactions are useful to reproduce various patterns corresponding to such detailed microscopic information. However, the approach is inconvenient for observing the specific mechanisms behind the target phenomena because of the compression of the information. Therefore, we previously proposed a method capable of approximating any nonlocal interactions by a reaction–diffusion system with auxiliary factors (Ninomiya et al., J Math Biol 75:1203–1233, 2017). In this paper, we provide an explicit method for determining the parameters of the reaction–diffusion system for the given kernel shape by using Jacobi polynomials under appropriate assumptions. We additionally introduce a numerical method to specify the parameters of the reaction–diffusion system with the general diffusion coefficients by the Tikhonov regularization.