Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

Rory A Locke; John R Mahoney; Kevin A Mitchell

doi:10.1063/1.5004699

Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

Chaos. 2018 Jan;28(1):013129. doi: 10.1063/1.5004699.

Authors

Rory A Locke¹, John R Mahoney², Kevin A Mitchell¹

Affiliations

¹ School of Natural Sciences, University of California, Merced, California 95344, USA.
² Department of Physics, University of California, Davis, California 95616, USA.

PMID: 29390612
DOI: 10.1063/1.5004699

Abstract

Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.