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Approximate analytical solutions of Schnakenberg systems by homotopy analysis method

机译：用同伦分析法求解Schnakenberg系统的近似解析解。

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In this paper, the homotopy analysis method (HAM) has been employed to obtain analytical solution of a two reaction-diffusion systems of fractional order (fractional Schnakenberg systems) which has been modeling morphogen systems in developmental biology. Different from all other analytic methods, HAM provides us with a simple way to adjust and control the convergence region of solution series by choosing proper values for auxiliary parameter h. The fractional derivative is described in the Caputo sense. The reason of using fractional order differential equations (FOD) is that FOD are naturally related to systems with memory which exists in most biological systems. Also they are closely related to fractals which are abundant in biological systems. The results derived of the fractional system are of a more general nature. Respectively, solutions of FOD spread at a faster rate than the classical differential equations, and may exhibit asymmetry. However, the fundamental solutions of these equations still exhibit useful scaling properties that make them attractive for applications.
机译：在本文中，同构分析方法（HAM）已用于获得两个分数阶反应扩散系统（分数Schnakenberg系统）的解析解，该系统已经在发育生物学中对形态发生子系统进行了建模。与所有其他分析方法不同，HAM通过为辅助参数h选择合适的值为我们提供了一种简单的方法来调整和控制解序列的收敛区域。分数导数在Caputo的意义上进行了描述。使用分数阶微分方程（FOD）的原因是，FOD与大多数生物系统中存在的具有记忆的系统自然相关。它们也与生物系统中丰富的分形密切相关。分数系统得出的结果具有更一般的性质。 FOD的解分别以比经典微分方程更快的速度扩展，并且可能表现出不对称性。但是，这些方程式的基本解仍然显示出有用的缩放属性，这使其对应用程序具有吸引力。

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