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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Parametric instability-induced synchronization in chemical oscillations and spatiotemporal patterns
Shibashis Paul1, Krishnendu Pal1, Deb Shankar Ray1
1Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India.
Physical Review. E
|December 17, 2020
Summary
Parametric instability in coupled reaction-diffusion systems drives synchronization and pattern formation. This study analytically and numerically reveals antiphase synchronization and spatiotemporal patterns above critical forcing and coupling thresholds.
Area of Science:
- Chemical kinetics
- Nonlinear dynamics
- Mathematical modeling
Background:
- Reaction-diffusion systems are fundamental to understanding pattern formation and oscillations in chemical and biological systems.
- Parametric driving introduces external periodic forces that can destabilize stable states and lead to novel dynamics.
- Coupled layers in such systems allow for complex emergent behaviors like synchronization.
Purpose of the Study:
- To investigate the phenomenon of parametric instability in a two-layer reaction-diffusion system.
- To analytically derive critical thresholds for instability and synchronization.
- To explore the emergence of spatiotemporal patterns and antiphase synchronization.
Main Methods:
- Analytical formulation of a general scheme to derive critical thresholds and dispersion relations.
- Perturbation analysis of a homogeneous stable steady state.
- Full numerical simulations using the Gierer-Meinhardt activator-inhibitor model.
Main Results:
- Parametric instability induces synchronization of temporal oscillations at half the forcing frequency (in the absence of diffusion).
- Spatiotemporal patterns emerge in the presence of diffusion when forcing and coupling exceed critical thresholds.
- Analytical predictions for critical thresholds and unstable spatial modes are corroborated by numerical simulations.
Conclusions:
- Parametric instability is a key mechanism for inducing antiphase synchronization and spatiotemporal pattern formation in coupled reaction-diffusion systems.
- The study provides a theoretical framework and numerical validation for understanding these complex dynamics.
- Findings are relevant to chemical oscillations and pattern formation in spatially extended systems.
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