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 piecewise 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 piecewise constant kinetic parameters and, as such, may be analyzed 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 induced.

Department of Mathematics FNSPE Czech Technical University Prague Prague Czech Republic

Wolfson Centre for Mathematical Biology Mathematical Institute University of Oxford United Kingdom

References provided by Crossref.org

Modern perspectives on near-equilibrium analysis of Turing systems

Isolating Patterns in Open Reaction-Diffusion Systems

Turing Patterning in Stratified Domains

From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ