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Keywords
reactiondiffusion Turing patterns
Schnakenberg reaction mechanism
How to Cite
Abstract
In this paper we present several numerical tests on reaction-diffusion equations in the space of Turing, under the Schnakenberg reaction mechanism. The tests were performed on 2D unit square, to which is imposed on random initial conditions and Neumann zero on the boundary. The parameters that define the behavior of the equations are modeled as stochastic fields, specifically, are used: the diffusion and reactive parameters as values of random type. Thus, combines the standard method of finite element Newton-Raphson with the finite element method spectral stochastic. The parameters of each equation described by Karhunen-Loève expansion, while the unknown is represented by the expansion of the polynomials of chaos. The objective of this article is to obtain the patterns of each coefficient of the polynomial chaos expansion. The results show the versatility of the method to solve different physical problems. Furthermore, it achieves statistical description of the solution. The results (for the unknown coefficients stochastic) show bands complex patterns and mixing points, which can not be predicted from the dynamics of the system.
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