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.
Bibliographical noteFunding Information:
The work by M.I.C. and M.F. was financed by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia—within Project Nos. UIDB/50014/2020, UIDB/50025/2020, UIDP/50025/2020, and LA/P/0037/2020. O.D. and C.C. wish to acknowledge the support of FONDECYT (CL) (No. 1200357) and Universidad de los Andes through FAI initiatives. H.R.B. thanks the Deutsche Forschungsgemeinschaft (DE) for partial support of this work.
© 2023 Author(s).