{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:19:36Z","timestamp":1753874376593,"version":"3.41.2"},"reference-count":50,"publisher":"AIP Publishing","issue":"8","funder":[{"name":"Portuguese funding agency, FCT","award":["UIDB\/50014\/2020"],"award-info":[{"award-number":["UIDB\/50014\/2020"]}]},{"name":"Portuguese funding agency, FCT","award":["UIDB\/50025\/2020"],"award-info":[{"award-number":["UIDB\/50025\/2020"]}]},{"name":"Portuguese funding agency, FCT","award":["UIDP\/50025\/2020"],"award-info":[{"award-number":["UIDP\/50025\/2020"]}]},{"name":"Portuguese funding agency, FCT","award":["LA\/P\/0037\/2020"],"award-info":[{"award-number":["LA\/P\/0037\/2020"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"FONDECYT","award":["1200357"],"award-info":[{"award-number":["1200357"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,8,1]]},"abstract":"<jats:p>We investigate the properties of time-dependent dissipative solitons for a cubic complex Ginzburg\u2013Landau 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.<\/jats:p>","DOI":"10.1063\/5.0156518","type":"journal-article","created":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T15:25:41Z","timestamp":1692977141000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Characterization of time-dependence for dissipative solitons stabilized by nonlinear gradient terms: Periodic and quasiperiodic vs chaotic behavior"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3474-0181","authenticated-orcid":false,"given":"Orazio","family":"Descalzi","sequence":"first","affiliation":[{"name":"Complex Systems Group, Facultad de Ingenier\u00eda y Ciencias Aplicadas, Universidad de los Andes 1 , Av. Mons. \u00c1lvaro del Portillo 12.455, Las Condes, Santiago, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2417-6743","authenticated-orcid":false,"given":"M.","family":"Fac\u00e3o","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade de Aveiro and I3N Campus Universit\u00e1rio de Santiago 2 , 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6770-4983","authenticated-orcid":false,"given":"Carlos","family":"Cartes","sequence":"additional","affiliation":[{"name":"Complex Systems Group, Facultad de Ingenier\u00eda y Ciencias Aplicadas, Universidad de los Andes 1 , Av. Mons. \u00c1lvaro del Portillo 12.455, Las Condes, Santiago, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6603-7928","authenticated-orcid":false,"given":"M. I.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"INESC TEC and DEEC\/FEUP, Universidade do Porto 3 , Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0459-4865","authenticated-orcid":false,"given":"Helmut R.","family":"Brand","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Bayreuth 4 , 95440 Bayreuth, Germany"}]}],"member":"317","published-online":{"date-parts":[[2023,8,25]]},"reference":[{"key":"2023082515244400700_c1","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1103\/PhysRevLett.15.240","volume":"18","year":"1965","journal-title":"Phys. Rev. Lett."},{"volume-title":"Solitons in Mathematics and Physics","year":"1985","key":"2023082515244400700_c2"},{"key":"2023082515244400700_c3","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1103\/RevModPhys.65.851","volume":"65","year":"1993","journal-title":"Rev. Mod. 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