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

Source: [Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics](<https://www.sota2.com/research/paper/68fa3ad61e209131ce8cdf88>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:17:41.495Z

Authors: Michal Koz\\'ak, Eamonn A Gaffney, V\\'aclav Klika

Published: 2019-08-26T06:47:49.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1908.09495>)

[PDF](<https://arxiv.org/pdf/1908.09495.pdf>)