O. Descalzi, M. Facão, C. Cartes, M. Carvalho, H. Brand
{"title":"非线性梯度项稳定的耗散孤子的时间依赖性表征:周期和准周期与混沌行为","authors":"O. Descalzi, M. Facão, C. Cartes, M. Carvalho, H. Brand","doi":"10.1063/5.0156518","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":340975,"journal":{"name":"Chaos: An Interdisciplinary Journal of Nonlinear Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterization of time-dependence for dissipative solitons stabilized by nonlinear gradient terms: Periodic and quasiperiodic vs chaotic behavior\",\"authors\":\"O. Descalzi, M. Facão, C. Cartes, M. Carvalho, H. Brand\",\"doi\":\"10.1063/5.0156518\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":340975,\"journal\":{\"name\":\"Chaos: An Interdisciplinary Journal of Nonlinear Science\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos: An Interdisciplinary Journal of Nonlinear Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0156518\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos: An Interdisciplinary Journal of Nonlinear Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0156518","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Characterization of time-dependence for dissipative solitons stabilized by nonlinear gradient terms: Periodic and quasiperiodic vs chaotic behavior
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.