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Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective
Rory A Locke1, John R Mahoney2, Kevin A Mitchell1
1School of Natural Sciences, University of California, Merced, California 95344, USA.
Chaos (Woodbury, N.Y.)
|February 3, 2018
Summary
Reaction fronts in 2D systems can synchronize with fluid flow frequencies, a phenomenon explained by burning invariant manifolds (BIMs) linked to relative periodic orbits (RPOs). Bifurcations of RPOs and BIMs govern changes in this mode-locking behavior.
Area of Science:
- Complex systems dynamics
- Fluid dynamics
- Chemical reaction kinetics
Background:
- Advection-reaction-diffusion systems display complex front propagation.
- Periodic fluid flows can influence reaction front behavior, leading to phenomena like mode-locking.
- Understanding front dynamics is crucial in various scientific fields.
Purpose of the Study:
- To elucidate the mechanism behind reaction front mode-locking in periodic flows.
- To introduce burning invariant manifolds (BIMs) as a tool for analyzing mode-locking.
- To explain mode-locking changes via bifurcations of relative periodic orbits (RPOs).
Main Methods:
- Theoretical analysis using burning invariant manifolds (BIMs).
- Numerical simulations of reaction fronts in a 2D channel with alternating vortices.
- Investigation of local and global bifurcations of RPOs and BIMs.
Main Results:
- Mode-locking of reaction fronts is explained by BIMs attached to RPOs.
- The dynamics of mode-locking changes are linked to bifurcations of these RPOs and BIMs.
- Numerical examples demonstrate these concepts in a specific vortex flow geometry.
Conclusions:
- BIMs and RPOs provide a robust framework for understanding reaction front mode-locking.
- Bifurcation theory effectively describes transitions in mode-locking behavior.
- The study offers insights into pattern formation and synchronization in complex systems.
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