@article{ref1,
title="Intermittent explosions of dissipative solitons and noise-induced crisis",
journal="Physical review E: Statistical, nonlinear, and soft matter physics",
year="2013",
author="Cisternas, Jaime and Descalzi, Orazio",
volume="88",
number="2",
pages="022903-022903",
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.<p /> <p>Language: en</p>",
language="en",
issn="1539-3755",
doi="",
url="http://dx.doi.org/"
}