Collective phase description of oscillatory convection.

@article{Kawamura2011CollectivePD,
  title={Collective phase description of oscillatory convection.},
  author={Yoji Kawamura and Hiroya Nakao},
  journal={Chaos},
  year={2011},
  volume={23 4},
  pages={
          043129
        }
}
We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the… 

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