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arXiv · 1908.09495

Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics

Michal Kozák·Eamonn A Gaffney·Václav Klika
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Abstract

The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction kinetics by exploring the effect of a jump discontinuity within piece-wise constant kinetic parameters, using various methods to identify and confirm the diffusion-driven instability conditions. Essentially, the presence of stability or instability in Turing models is a local property for piece-wise constant kinetic parameters and, as such, may be analysed locally. In particular, a local assessment of whether parameters are within the Turing space provides a strong indication that for a large enough region with these parameters, an instability can be excited.

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Michal Kozák, Eamonn A Gaffney, Václav Klika. 2019-08-26. Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics. https://doi.org/10.1103/physreve.100.042220

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