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Time-Periodic Forcing of Spatially Localized Structures

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Nonlinear Dynamics: Materials, Theory and Experiments

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 173))

Abstract

We study localized states in the Swift–Hohenberg equation when time-periodic parametric forcing is introduced. The presence of a time-dependent forcing introduces a new characteristic time which creates a series of resonances with the depinning time of the fronts bounding the localized pattern. The organization of these resonances in parameter space can be understood using appropriate asymptotics. A number of distinct canard trajectories involved in the observed transitions is constructed.

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Acknowledgments

This work was supported by the National Science Foundation under grant CMMI–1233692.

Author information

Authors and Affiliations

  1. Department of Physics, University of California, Berkeley, CA, 94720, USA

    Punit Gandhi & Edgar Knobloch

  2. Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK

    Cédric Beaume

Authors
  1. Punit Gandhi
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  2. Cédric Beaume
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  3. Edgar Knobloch
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Corresponding author

Correspondence to Punit Gandhi .

Editor information

Editors and Affiliations

  1. Physique des systèmes dynamiques, Université Libre de Bruxelles, Brussels, Belgium

    Mustapha Tlidi

  2. Universidad de Chile, Santiago, Chile

    Marcel. G. Clerc

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Gandhi, P., Beaume, C., Knobloch, E. (2016). Time-Periodic Forcing of Spatially Localized Structures. In: Tlidi, M., Clerc, M. (eds) Nonlinear Dynamics: Materials, Theory and Experiments. Springer Proceedings in Physics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-24871-4_23

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