Citation

Cisternas J, Descalzi O. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2013; 88(2): 022903.

Affiliation

Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Avenida Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile.

Copyright

(Copyright © 2013, American Physical Society, Publisher American Institute of Physics)

DOI

unavailable

PMID

24032897

Abstract

Dissipative solitons show a variety of behaviors not exhibited by their conservative counterparts. For instance, a dissipative soliton can remain localized for a long period of time without major profile changes, then grow and become broader for a short time-explode-and return to the original spatial profile afterward. Here we consider the dynamics of dissipative solitons and the onset of explosions in detail. By using the one-dimensional complex Ginzburg-Landau model and adjusting a single parameter, we show how the appearance of explosions has the general signatures of intermittency: the periods of time between explosions are irregular even in the absence of noise, but their mean value is related to the distance to criticality by a power law. We conjecture that these explosions are a manifestation of attractor-merging crises, as the continuum of localized solitons induced by translation symmetry becomes connected by short-lived trajectories, forming a delocalized attractor. As additive noise is added, the extended system shows the same scaling found by low-dimensional systems exhibiting crises [J. Sommerer, E. Ott, and C. Grebogi, Phys. Rev. A 43, 1754 (1991)], thus supporting the validity of the proposed picture.

Language: en