Dissipative solitons and their critical slowing down near a supercritical bifurcation

Bakonyi, Z.; Michaelis, Dirk; Peschel, Ulf; Onishchukov, G.; Lederer, F.

doi:10.1364/josab.19.000487

Cited by 50 publications

(8 citation statements)

References 16 publications

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“…Examples include pulse generation by passively mode-locked soliton lasers [4], signal transmission in all-optical communication lines [5], travelling waves in binary fluid mixtures [6], and also pattern formation in many other physical systems [7]. Complicated patterns consist of simpler localized solutions like fronts, pulses, sources and sinks [8].…”

mentioning

confidence: 99%

Bifurcations from stationary to pulsating solitons in the cubic–quintic complex Ginzburg–Landau equation

Tsoy

Akhmediev

2005

Physics Letters A

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Stationary to pulsating soliton bifurcation analysis of the complex Ginzburg-Landau equation (CGLE) is presented. The analysis is based on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. Stationary solitons, with constant amplitude and width, are associated with fixed points in the model. For the first time, pulsating solitons are shown to be stable limit cycles in the finite-dimensional dynamical system. The boundaries between the two types of solutions are obtained approximately from the reduced model. These boundaries are reasonably close to those predicted by direct numerical simulations of the CGLE.

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confidence: 99%

Bifurcations from stationary to pulsating solitons in the cubic–quintic complex Ginzburg–Landau equation

Tsoy

Akhmediev

2005

Physics Letters A

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“…Importantly, the auxiliary parameter G increases with the number of choices M, see (49). Therefore, the question arises how does the time T depend on the factor G. Differentiating T with respect to G yields…”

Section: Discussionmentioning

confidence: 99%

“…In experimental studies, such critical phenomena have been found in the inanimate world and the life sciences. For example, critical phenomena have been observed during the emergence of roll patterns in fluid layers heated from below [46][47][48] and in optical systems in which so-called dissipative solitons emerge due to self-organization [49]. Likewise, they have been found in experiments on human motor coordination, in which participants switched between two distinct motor coordination modes [50][51][52][53][54][55].…”

Section: Phenomena/subtopicsmentioning

confidence: 94%

Interplay between order-parameter and system parameter dynamics: considerations on perceptual-cognitive-behavioral mode-mode transitions exhibiting positive and negative hysteresis and on response times

Frank

Profeta²,

Harrison

2015

J Biol Phys

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A mathematical model is presented for the emergence of perceptual-cognitivebehavioral modes in psychophysical experiments in which participants are confronted with two alternatives. The model is based on the theory of self-organization and, in particular, the order parameter concept such that the emergence of a mode is conceptualized as an instability leading to the emergence of an appropriately defined order parameter. The order parameter model is merged with a second model that describes adaptation in terms of a system parameter dynamics. It is shown that the two-component model predicts hysteretic mode-mode transitions when control parameters are increased or decreased beyond critical values. The two-component model can account for both positive and negative hysteresis effects due to the interaction between order parameter and system parameter dynamics. Moreover, the model-based analysis reveals that response time curves look rather flat when response times are relatively decoupled from the mode-mode transition phenomenon. In general, response time curves exhibit a peaked close to the mode-mode transition point. In this context, the possibility is discussed that such peaked response time curves belong to the class of critical phenomena of self-organizing systems. In order to illustrate the relevance of peaked response time curves for future research and research reported in the past, results from a perceptual judgment experiment are reported, in which participants judged their ability to stand on a tilted slope for various angles of inclination. Response time curves were found that exhibited a peak around the mode-mode-transition points between "yes" and "no" responses.

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“…The complex Ginzburg-Landau equation (CGLE) is a general model for dissipative systems, describing a vast variety of nonlinear phenomena in physics [11]. In particular, it describes pulse generation by passively mode-locked soliton lasers [12] and signal transmission in all-optical communication lines [13]. In dimensionless form, the CGLE is [7,14]…”

Section: Introductionmentioning

confidence: 99%

Dissipative solitons with a Lagrangian approach

Ankiewicz

Akhmediev

Devine

2007

Optical Fiber Technology

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Dissipative solitons and their critical slowing down near a supercritical bifurcation

Cited by 50 publications

References 16 publications

Bifurcations from stationary to pulsating solitons in the cubic–quintic complex Ginzburg–Landau equation

Bifurcations from stationary to pulsating solitons in the cubic–quintic complex Ginzburg–Landau equation

Interplay between order-parameter and system parameter dynamics: considerations on perceptual-cognitive-behavioral mode-mode transitions exhibiting positive and negative hysteresis and on response times

Dissipative solitons with a Lagrangian approach

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