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Perturbations and dynamics of reaction-diffusion systems with mass conservation
Masataka Kuwamura1, Yoshihisa Morita2
1Graduate School of Human Development and Environment, Kobe University, Kobe 657-8501, Japan.
Summary
This study explores reaction-diffusion systems, revealing that even stable systems can generate large Turing-like patterns during transitions. A new model demonstrates alternating homogeneous oscillations and these complex spatial patterns.
Area of Science:
- Mathematical Biology
- Chemical Kinetics
- Pattern Formation
Background:
- Reaction-diffusion systems conserve total mass.
- Near equilibrium, solutions can form localized patterns (spikes).
- Turing-like patterns emerge for specific diffusion coefficients.
Purpose of the Study:
- Investigate perturbed reaction-diffusion systems with conserved mass.
- Analyze transient dynamics in models with stable homogeneous equilibria.
- Develop a model exhibiting complex pattern dynamics.
Main Methods:
- Analysis of conserved reaction-diffusion systems.
- Perturbation analysis of system dynamics.
- Development and simulation of a three-component model.
Main Results:
- Perturbed conserved systems can exhibit large amplitude Turing-like patterns transiently.
- A globally stable homogeneous equilibrium does not preclude large transient patterns.
- The proposed three-component model shows alternating homogeneous oscillations and Turing-like patterns.
Conclusions:
- Reaction-diffusion systems exhibit richer transient dynamics than previously assumed.
- Complex spatial patterns can arise even from stable homogeneous states.
- New models can capture intricate spatio-temporal behaviors in chemical and biological systems.
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