We investigate the properties of time-dependent dissipative solitons for a cubic complex Ginzburg–Landau equation stabilized by nonlinear gradient terms. The separation of initially nearby trajectories in the asymptotic limit is predominantly used to distinguish qualitatively between time-periodic behavior and chaotic localized states. These results are further corroborated by Fourier transforms and time series. Quasiperiodic behavior is obtained as well, but typically over a fairly narrow range of parameter values. For illustration, two examples of nonlinear gradient terms are examined: the Raman term and combinations of the Raman term with dispersion of the nonlinear gain. For small quintic perturbations, it turns out that the chaotic localized states are showing a transition to periodic states, stationary states, or collapse already for a small magnitude of the quintic perturbations. This result indicates that the basin of attraction for chaotic localized states is rather shallow.
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August 2023
Research Article|
August 25 2023
Characterization of time-dependence for dissipative solitons stabilized by nonlinear gradient terms: Periodic and quasiperiodic vs chaotic behavior
Orazio Descalzi
;
Orazio Descalzi
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing)
1
Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes
, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago, Chile
a)Author to whom correspondence should be addressed: odescalzi@miuandes.cl
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M. Facão
;
M. Facão
(Conceptualization, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
2
Departamento de Física, Universidade de Aveiro and I3N Campus Universitário de Santiago
, 3810-193 Aveiro, Portugal
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Carlos Cartes
;
Carlos Cartes
(Investigation, Software, Writing – original draft, Writing – review & editing)
1
Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes
, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago, Chile
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M. I. Carvalho
;
M. I. Carvalho
(Conceptualization, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing)
3
INESC TEC and DEEC/FEUP, Universidade do Porto
, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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Helmut R. Brand
Helmut R. Brand
(Conceptualization, Formal analysis, Investigation, Methodology, Supervision, Validation, Writing – original draft, Writing – review & editing)
4
Department of Physics, University of Bayreuth
, 95440 Bayreuth, Germany
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a)Author to whom correspondence should be addressed: odescalzi@miuandes.cl
Chaos 33, 083151 (2023)
Article history
Received:
April 30 2023
Accepted:
August 07 2023
Citation
Orazio Descalzi, M. Facão, Carlos Cartes, M. I. Carvalho, Helmut R. Brand; Characterization of time-dependence for dissipative solitons stabilized by nonlinear gradient terms: Periodic and quasiperiodic vs chaotic behavior. Chaos 1 August 2023; 33 (8): 083151. https://doi.org/10.1063/5.0156518
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