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Localized states in periodically forced systems.

Punit Gandhi1, Edgar Knobloch1, Cédric Beaume2

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

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Summary
This summary is machine-generated.

Time-periodic forcing creates complex localized patterns in dissipative systems. These dynamic structures arise from competing nucleation and annihilation processes, revealing resonances with the forcing period.

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Area of Science:

  • Nonlinear dynamics
  • Pattern formation in dissipative systems
  • Theoretical physics

Background:

  • Stationary localized patterns in dissipative systems under constant forcing are well-understood.
  • Time-periodic forcing introduces complex, time-dependent structures.
  • These dynamic states can exhibit 'breathing' or growth/annihilation cycles.

Purpose of the Study:

  • Investigate the behavior of localized patterns in dissipative systems subjected to time-periodic forcing.
  • Analyze the formation of complex, time-dependent structures.
  • Understand the underlying mechanisms and phase diagram of these systems.

Main Methods:

  • Utilized the periodically forced quadratic-cubic Swift-Hohenberg equation as a model system.
  • Computed the complex phase diagram of the system's behavior.
  • Interpreted the phase diagram in terms of depinning transitions of pattern fronts.

Main Results:

  • Identified complex phase diagrams arising from competing nucleation and annihilation processes.
  • Demonstrated that the phase diagram structure is linked to resonances between nucleation time and forcing period.
  • Characterized the role of depinning transitions of fronts bounding the localized states.

Conclusions:

  • Time-periodic forcing leads to rich and complex localized pattern dynamics.
  • The interplay between nucleation and annihilation, governed by resonances, dictates pattern behavior.
  • Findings offer insights into localized states across various periodically driven systems.