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Pattern formation in reaction-diffusion systems with piecewise kinetic modulation: An example study of heterogeneous
Michal Kozák1, Eamonn A Gaffney2, Václav Klika1
1Department of Mathematics, FNSPE, Czech Technical University in Prague, Prague, Czech Republic.
Physical Review. E
|November 28, 2019
Summary
This study analyzes pattern emergence in Turing models by examining stability with discontinuous parameters. Local analysis of kinetic parameters can predict diffusion-driven instabilities for pattern formation.
Area of Science:
- Reaction-diffusion systems
- Mathematical biology
- Pattern formation
Background:
- Turing models are fundamental to understanding pattern emergence.
- A theoretical and experimental renaissance is occurring in Turing model research.
- The stability of these models is crucial for pattern formation.
Purpose of the Study:
- To perform a stability analysis of spatially dependent reaction kinetics.
- To investigate the impact of jump discontinuities in piecewise constant kinetic parameters.
- To identify and confirm conditions for diffusion-driven instability in Turing models.
Main Methods:
- Implementing a stability analysis for reaction kinetics.
- Exploring the effect of jump discontinuities in kinetic parameters.
- Utilizing various methods to identify diffusion-driven instability conditions.
Main Results:
- Stability or instability in Turing models is a local property for piecewise constant parameters.
- Local assessment of parameters within the Turing space indicates potential for induced instability.
- Discontinuities in kinetic parameters can be analyzed locally to predict stability.
Conclusions:
- Local analysis of kinetic parameters is sufficient to determine stability in Turing models.
- Understanding parameter regions within the Turing space is key to predicting pattern formation.
- The study confirms the role of diffusion-driven instabilities in pattern emergence.
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