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Turing instability in reaction-subdiffusion systems.

A Yadav1, Shane M Milu, Werner Horsthemke

  • 1Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

Turing instabilities in activator-inhibitor systems are affected by diffusion types. Subdiffusion in species with nonlinear death rates can advance or delay pattern formation, depending on whether the inhibitor or activator subdiffuses.

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Area of Science:

  • Chemical kinetics
  • Non-equilibrium thermodynamics
  • Pattern formation

Background:

  • Turing instabilities drive pattern formation in activator-inhibitor systems.
  • Anomalous diffusion, such as subdiffusion, can alter reaction-diffusion dynamics.
  • Non-Markovian processes introduce memory effects impacting system evolution.

Purpose of the Study:

  • To determine conditions for Turing instabilities in systems with mixed diffusion (subdiffusion and normal diffusion).
  • To investigate how nonlinear kinetics and subdiffusion memory effects influence pattern formation.
  • To analyze the impact of subdiffusion on activator and inhibitor roles in instability onset.

Main Methods:

  • Mathematical analysis of activator-inhibitor models with subdiffusion and normal diffusion.
  • Investigation of non-Markovian transport effects on reaction-diffusion equations.
  • Application of theoretical findings to established models like Schnakenberg, Gray-Scott, Oregonator, and Lengyel-Epstein.

Main Results:

  • Subdiffusion coupled with nonlinear death rates alters Turing instability onset.
  • If the inhibitor subdiffuses, Turing instability is advanced.
  • If the activator subdiffuses, Turing instability is delayed.

Conclusions:

  • The interplay between nonlinear kinetics and subdiffusion memory effects is crucial for pattern formation.
  • Subdiffusion can significantly shift the conditions for pattern emergence in chemical systems.
  • Findings provide insights into diverse reaction-diffusion systems exhibiting anomalous transport.