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Examples of the Effect of Growth and Strain on Turing Pattern Formation Dynamics

Reaction–diffusion (RD) equation behavior has been studied in various fields, including biology, bioengineering and chemistry. Their solution leads to the formation of patterns which are stable in time and unstable in space, especially when RD system parameters are in the Turing space. Such patterns can be changed due to the growth of the domain where the reaction takes place. This article presents RD equations concerning growing domains in 2D and 3D. Several numerical examples have been solved using different geometries to study the effect of growth on pattern formation. The finite element method was used in conjunction with the Newton–Raphson method for the numerical solution to approximate nonlinear partial differential equations. It was found that growth affected Turing pattern formation, thereby generating complex structures in the domain.