Collective phase description of oscillatory convection

Details Collective phase description of oscillatory convection Collective phase description of oscillatory convection

2011-10-06

arxiv.org/abs/1110.1128v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

14 pages, 4 figures

Scientific paper

We formulate a theory of collective phase description for oscillatory convection in Hele-Shaw cells. The theory can be considered a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, time-periodic solutions to partial differential equations representing oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of an oscillatory convection to weak perturbations applied at each spatial point. Using the phase sensitivity function, we analyze phase synchronization between two weakly coupled oscillatory convections.

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