Localized chaotic patterns in weakly dissipative systems

Deterlino Alberto Urzagasti Guerrero Urzagasti Guerrero; D. Laroze; H. Pleiner

doi:10.1140/epjst/e2014-02089-x

Localized chaotic patterns in weakly dissipative systems

Deterlino Alberto Urzagasti Guerrero Urzagasti Guerrero, D. Laroze, H. Pleiner

Resultado de la investigación: Contribución a una revista › Artículo › revisión exhaustiva

13 Citas (Scopus)

Resumen

A generalized parametrically driven damped nonlinear Schrödinger equation is used to describe, close to the resonance, the dynamics of weakly dissipative systems, like a harmonically coupled pendula chain or an easy-plane magnetic wire. The combined effects of parametric forcing, spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found. We discuss the parameter range, where these localized structures exist. This article is dedicated to Prof. Helmut R. Brand on the occasion of his 60th birthday.

Idioma original	Inglés
Páginas (desde-hasta)	141-154
Número de páginas	14
Publicación	European Physical Journal: Special Topics
Volumen	223
N.º	1
DOI	https://doi.org/10.1140/epjst/e2014-02089-x
Estado	Publicada - ene. 2014
Publicado de forma externa	Sí

Nota bibliográfica

Funding Information:
D.U. and D.L. would like to thank M.G. Clerc (Univ. of Chile) for valuable discussions on the generalization of the PDDNLS equation. D. L. acknowledges partial financial support from FONDECYT 1120764, Millennium Scientific Initiative, P10−061−F, Basal Program Center for Development of Nanoscience and Nanotechnology (CEDENNA), UTA-project 8750−12. D. U. acknowledges the PhD program fellowship through the Performance Agreement Project’s UTA/Mineduc.

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title = "Localized chaotic patterns in weakly dissipative systems",

abstract = "A generalized parametrically driven damped nonlinear Schr{\"o}dinger equation is used to describe, close to the resonance, the dynamics of weakly dissipative systems, like a harmonically coupled pendula chain or an easy-plane magnetic wire. The combined effects of parametric forcing, spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found. We discuss the parameter range, where these localized structures exist. This article is dedicated to Prof. Helmut R. Brand on the occasion of his 60th birthday.",

author = "{Urzagasti Guerrero}, {Deterlino Alberto Urzagasti Guerrero} and D. Laroze and H. Pleiner",

note = "Funding Information: D.U. and D.L. would like to thank M.G. Clerc (Univ. of Chile) for valuable discussions on the generalization of the PDDNLS equation. D. L. acknowledges partial financial support from FONDECYT 1120764, Millennium Scientific Initiative, P10−061−F, Basal Program Center for Development of Nanoscience and Nanotechnology (CEDENNA), UTA-project 8750−12. D. U. acknowledges the PhD program fellowship through the Performance Agreement Project{\textquoteright}s UTA/Mineduc.",

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doi = "10.1140/epjst/e2014-02089-x",

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AU - Urzagasti Guerrero, Deterlino Alberto Urzagasti Guerrero

AU - Laroze, D.

AU - Pleiner, H.

N1 - Funding Information: D.U. and D.L. would like to thank M.G. Clerc (Univ. of Chile) for valuable discussions on the generalization of the PDDNLS equation. D. L. acknowledges partial financial support from FONDECYT 1120764, Millennium Scientific Initiative, P10−061−F, Basal Program Center for Development of Nanoscience and Nanotechnology (CEDENNA), UTA-project 8750−12. D. U. acknowledges the PhD program fellowship through the Performance Agreement Project’s UTA/Mineduc.

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N2 - A generalized parametrically driven damped nonlinear Schrödinger equation is used to describe, close to the resonance, the dynamics of weakly dissipative systems, like a harmonically coupled pendula chain or an easy-plane magnetic wire. The combined effects of parametric forcing, spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found. We discuss the parameter range, where these localized structures exist. This article is dedicated to Prof. Helmut R. Brand on the occasion of his 60th birthday.

AB - A generalized parametrically driven damped nonlinear Schrödinger equation is used to describe, close to the resonance, the dynamics of weakly dissipative systems, like a harmonically coupled pendula chain or an easy-plane magnetic wire. The combined effects of parametric forcing, spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found. We discuss the parameter range, where these localized structures exist. This article is dedicated to Prof. Helmut R. Brand on the occasion of his 60th birthday.

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JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

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Localized chaotic patterns in weakly dissipative systems

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