Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Pattern Formation

DY 15.10: Talk

Tuesday, April 2, 2019, 12:30–12:45, H3

Pattern formation of a coupled Turing-polarity model — •Francine Kolley¹, Peter Groß¹, K Vijay Kumar², and Stephan W Grill¹ — ¹BIOTEC, TU Dresden, Germany — ²ICTS, Bangalore, India

Pattern formations are ubiquitous phenomena in nature. It is the ability of non-equilibrium systems to form stable, spatially non-homogeneous states. Such non-equilibrium patterns can emerge via a large class of distinct mechanisms.
Our aim is to couple two different mechanisms, Turing patterns and polarity patterns.
Turing systems are typically described using a diffusion term, which enables to spread out over the space and a reaction term, which couples two different species. These two species can establish Turing patterns under the condition of short-ranged activation and long-ranged inhibition.
In comparison to Turing systems, a central feature of polarity models is mass conservation. As a consequence, the patterned state generally has a singular domain. Furthermore, polarity models can show multistability, where the homogeneous state and the patterned state are both stable to perturbations.
We construct a model that can be gradually shifted from a pure Turing system to a pure polarity system. We investigate the pattern formation properties of this model, with a particular emphasis on the region where the Turing mode and the polarity mode compete.