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Stabilization of a spatially uniform steady state in two systems exhibiting Turing patterns
1Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan.
Physical Review. E
|June 17, 2018
Summary
This study explores amplitude death in coupled reaction-diffusion systems. Stabilization occurs when systems are non-identical, preventing uniform steady states.
Area of Science:
- Nonlinear dynamics
- Chemical kinetics
- Mathematical biology
Background:
- Reaction-diffusion systems exhibit complex spatio-temporal patterns.
- Turing instability can lead to pattern formation in these systems.
- Amplitude death is a phenomenon where coupled oscillators cease to oscillate.
Purpose of the Study:
- Investigate the stabilization of spatially uniform steady states in coupled reaction-diffusion systems.
- Analyze the conditions leading to amplitude death under Turing instability.
- Determine criteria for stabilization in non-identical coupled systems.
Main Methods:
- Stability analysis of the steady state.
- Derivation of analytical conditions for stabilization.
- Numerical simulations to support theoretical findings.
Main Results:
- Stabilization (amplitude death) does not occur if the two reaction-diffusion systems are identical.
- A sufficient condition for steady-state stability was derived, independent of system length and boundary conditions.
- Numerical examples validated the analytical results.
Conclusions:
- Non-identical coupled reaction-diffusion systems can achieve amplitude death.
- The derived condition provides a general criterion for stabilization in such systems.
- This work contributes to understanding pattern suppression in reaction-diffusion systems.
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