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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability
 Kůs, Pavel
In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problém are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.
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Irregularity of turing patterns in the Thomas model with a unilateral term
 Rybář, Vojtěch ; Vejchodský, Tomáš
In this contribution we add a unilateral term to the Thomas model and investigate the resulting Turing patterns. We show that the unilateral term yields nonsymmetric and irregular patterns. This contrasts with the approximately symmetric and regular patterns of the classical Thomas model. In addition, the unilateral term yields Turing patterns even for smaller ratio of diffusion constants. These conclusions accord with the recent findings about the influence of the unilateral term in a model for mammalian coat patterns. This indicates that the observed effects of the unilateral term are general and apply to a variety of systems.
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