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Noisy localized structures induced by large noise.

Orazio Descalzi1,2, Carlos Cartes1, Helmut R Brand2

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Large noise influences localized patterns in complex Ginzburg-Landau equations, creating noisy structures. This study explores noise-pattern interactions in subcritical conditions where stable pulses don't exist.

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Area of Science:

  • Nonlinear dynamics
  • Pattern formation
  • Complex systems

Background:

  • The cubic-quintic complex Ginzburg-Landau equation models various nonlinear phenomena.
  • Understanding noise effects is crucial for predicting pattern stability.
  • Deterministic localized structures may not exist in certain parameter regimes.

Purpose of the Study:

  • To investigate the impact of significant noise on localized pattern formation.
  • To analyze the interplay between noise and localization.
  • To explore pattern dynamics in subcritical parameter regions.

Main Methods:

  • Numerical simulations of the cubic-quintic complex Ginzburg-Landau equation.
  • Analysis of pattern formation under varying noise strengths.
  • Focus on parameter space where stable deterministic pulses are absent.

Main Results:

  • Noise can lead to the filling in of localized structures.
  • Noisy localized structures emerge with increasing noise intensity.
  • The system exhibits complex dynamics influenced by both localization and noise.

Conclusions:

  • Noise plays a significant role in shaping localized patterns.
  • The findings are relevant for systems exhibiting pattern formation in the presence of noise.
  • Potential experimental validation in chemical and biological systems is suggested.