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

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https://www.mitchellchaos.com/wp-content/uploads/2018/02/modelockingChaos.pdf
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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.

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