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Chaotic motion of localized structures.

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Summary
This summary is machine-generated.

Spatially localized structures in the bistable Swift-Hohenberg equation exhibit complex mobility and stability behaviors. Shorter structures show greater speed but are more fragile, with chaotic forcing impacting their dynamics and survival.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Computational physics

Background:

  • The bistable Swift-Hohenberg equation models pattern formation in various physical systems.
  • Understanding the dynamics of localized structures under external forcing is crucial.
  • Chaotic forcing introduces complex, deterministic perturbations unlike random white noise.

Purpose of the Study:

  • To investigate the mobility properties of localized structures driven by chaotic forcing.
  • To compare the effects of chaotic forcing with white noise forcing.
  • To analyze the stability of these structures under deterministic chaotic perturbations.

Main Methods:

  • Numerical simulations of the bistable Swift-Hohenberg equation with chaotic forcing.
  • Comparison of results with simulations using white noise forcing.
  • Quantification of structure mobility (speed, displacement) and stability regions.

Main Results:

  • Shorter localized structures exhibit higher mobility (greater root-mean-square speeds) but shorter displacements.
  • Structure displacement transitions from ballistic at short times to diffusive at longer times.
  • Shorter structures are less stable and more susceptible to destruction or growth under chaotic forcing.

Conclusions:

  • Chaotic forcing significantly influences the mobility and stability of localized structures.
  • Structure length is a critical parameter determining fragility and dynamic behavior.
  • The findings provide insights into pattern formation and stability in driven nonlinear systems.