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Updated: May 24, 2026
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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
Noise can induce explosions for dissipative solitons.
Carlos Cartes1, Orazio Descalzi, Helmut R Brand
1Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. San Carlos de Apoquindo 2200, Santiago, Chile.
Summary
Noise can induce chaotic behavior and exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation. Even small noise levels can trigger these explosions across a wide range of bifurcation parameters.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Mathematical Physics
Background:
- The cubic-quintic complex Ginzburg-Landau equation models various nonlinear phenomena.
- Understanding the impact of noise on localized states is crucial for predicting system behavior.
- Anomalous dispersion regimes present unique challenges for stability analysis.
Purpose of the Study:
- To investigate the influence of noise on stationary and periodic states.
- To analyze the emergence of chaotic behavior and exploding dissipative solitons.
- To determine the role of the bifurcation parameter in noise-induced transitions.
Main Methods:
- Numerical simulations of the cubic-quintic complex Ginzburg-Landau equation.
- Analysis of spatially localized, temporally regular states under varying noise levels.
- Utilizing separation diagnostics for chaotic behavior characterization.
- Employing energy analysis to detect explosive soliton dynamics.
Main Results:
- Small noise strengths (η) are sufficient to induce chaotic states with exploding dissipative solitons.
- Noise can trigger soliton explosions over a broad range of the bifurcation parameter (μ).
- Three distinct routes to chaos involving exploding dissipative solitons were identified as a function of μ.
Conclusions:
- Noise plays a significant role in destabilizing regular states and inducing chaos.
- Exploding dissipative solitons can be a common outcome in the presence of noise.
- The bifurcation parameter critically influences the pathways to noise-induced chaos.
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