scholarly journals Alternation of Defects and Phase Turbulence Induces Extreme Events in an Extended Microcavity Laser

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 789 ◽  
Author(s):  
Sylvain Barbay ◽  
Saliya Coulibaly ◽  
Marcel Clerc
Keyword(s):  
Extreme Events ◽  
Complex Dynamics ◽  
Dynamical Behavior ◽  
High Amplitude ◽  
Equation Model ◽  
Spatiotemporal Chaos ◽  
Ginzburg Landau ◽  
Microcavity Laser ◽  
Secondary Bifurcation ◽  
Secondary Instabilities

Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation.

scholarly journals Spatiotemporal Chaos Induces Extreme Events in an Extended Microcavity Laser

2016 ◽  
Vol 116 (1) ◽  
Author(s):  
F. Selmi ◽  
S. Coulibaly ◽  
Z. Loghmari ◽  
I. Sagnes ◽  
G. Beaudoin ◽  
...  
Keyword(s):  
Extreme Events ◽  
Spatiotemporal Chaos ◽  
Microcavity Laser

In–Out Intermittency with Nested Subspaces in a System of Globally Coupled, Complex Ginzburg–Landau Equations

2021 ◽  
Vol 31 (01) ◽  
pp. 2130001
Author(s):  
Gerhard Dangelmayr ◽  
Iuliana Oprea
Keyword(s):  
Normal Form ◽  
Traveling Waves ◽  
Complex Dynamics ◽  
Invariant Subspaces ◽  
Chaotic Attractors ◽  
Governing Equations ◽  
Ginzburg Landau ◽  
Higher Dimensional ◽  
Ginzburg Landau Equations ◽  
Anisotropic Systems

Chaos and intermittency are studied for the system of globally coupled, complex Ginzburg–Landau equations governing the dynamics of extended, two-dimensional anisotropic systems near an oscillatory (Hopf) instability of a basic state with two pairs of counterpropagating, oblique traveling waves. Parameters are chosen such that the underlying normal form, which governs the dynamics of the spatially constant modes, has two symmetry-conjugated chaotic attractors. Two main states residing in nested invariant subspaces are identified, a state referred to as Spatial Intermittency ([Formula: see text]) and a state referred to as Spatial Persistence ([Formula: see text]). The [Formula: see text]-state consists of laminar phases where the dynamics is close to a normal form attractor, without spatial variation, and switching phases with spatiotemporal bursts during which the system switches from one normal form attractor to the conjugated normal form attractor. The [Formula: see text]-state also consists of two symmetry-conjugated states, with complex spatiotemporal dynamics, that reside in higher dimensional invariant subspaces whose intersection forms the 8D space of the spatially constant modes. We characterize the repeated appearance of these states as (generalized) in–out intermittency. The statistics of the lengths of the laminar phases is studied using an appropriate Poincaré map. Since the Ginzburg–Landau system studied in this paper can be derived from the governing equations for electroconvection in nematic liquid crystals, the occurrence of in–out intermittency may be of interest in understanding spatiotemporally complex dynamics in nematic electroconvection.

Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation

1992 ◽  
Vol 57 (3-4) ◽  
pp. 241-248 ◽  
Author(s):  
B.I. Shraiman ◽  
A. Pumir ◽  
W. van Saarloos ◽  
P.C. Hohenberg ◽  
H. Chaté ◽  
...  
Keyword(s):  
Landau Equation ◽  
Spatiotemporal Chaos ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

scholarly journals SPATIOTEMPORAL CHAOS, LOCALIZED STRUCTURES AND SYNCHRONIZATION IN THE VECTOR COMPLEX GINZBURG–LANDAU EQUATION

1999 ◽  
Vol 09 (12) ◽  
pp. 2257-2264 ◽  
Author(s):  
EMILIO HERNÁNDEZ-GARCÍA ◽  
MIGUEL HOYUELOS ◽  
PERE COLET ◽  
MAXI SAN MIGUEL ◽  
RAÚL MONTAGNE
Keyword(s):  
Chaotic Dynamics ◽  
Landau Equation ◽  
Spatiotemporal Chaos ◽  
Quantitative Characterization ◽  
Ginzburg Landau ◽  
Information Measures ◽  
Localized Structures ◽  
Ginzburg Landau Equation ◽  
Spatial Dimensions

We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg–Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.

scholarly journals Modeling oscillations in connected glacial lakes

2019 ◽  
Vol 65 (253) ◽  
pp. 745-758 ◽  
Author(s):  
Aaron G. Stubblefield ◽  
Timothy T. Creyts ◽  
Jonathan Kingslake ◽  
Marc Spiegelman
Keyword(s):  
Complex Dynamics ◽  
Equation Model ◽  
Qualitative Behavior ◽  
Glacial Lakes ◽  
West Antarctica ◽  
Ice Streams ◽  
Mountain Glaciers ◽  
Lake Model ◽  
Dependent Model ◽  
Subglacial Lakes

AbstractMountain glaciers and ice sheets often host marginal and subglacial lakes that are hydraulically connected through subglacial drainage systems. These lakes exhibit complex dynamics that have been the subject of models for decades. Here we introduce and analyze a model for the evolution of glacial lakes connected by subglacial channels. Subglacial channel equations are supplied with effective pressure boundary conditions that are determined by a simple lake model. While the model can describe an arbitrary number of lakes, we solve it numerically with a finite element method for the case of two connected lakes. We examine the effect of relative lake size and spacing on the oscillations. Complex oscillations in the downstream lake are driven by discharge out of the upstream lake. These include multi-peaked and anti-phase filling–draining events. Similar filling–draining cycles have been observed on the Kennicott Glacier in Alaska and at the confluence of the Whillans and Mercer ice streams in West Antarctica. We further construct a simplified ordinary differential equation model that displays the same qualitative behavior as the full, spatially-dependent model. We analyze this model using dynamical systems theory to explain the appearance of filling–draining cycles as the meltwater supply varies.

A Study of the Influence of Bearing Clearance on Lateral Coupled Shaft/Disk Rotordynamics

1992 ◽  
Author(s):  
George T. Flowers ◽  
Fang Sheng Wu
Keyword(s):  
Dynamical Behavior ◽  
High Amplitude ◽  
Bladed Disk ◽  
Bearing Clearance ◽  
Shaft System ◽  
Coupling Dynamics ◽  
Bearing Loads ◽  
Rotating Flexible Disk ◽  
Flexible Disk ◽  
Clearance Nonlinearity

This study examines the influence of bearing clearance on the dynamical behavior of a rotating, flexible disk/shaft system. Most previous work in nonlinear rotordynamics has tended to concentrate separately on shaft vibration or on bladed disk vibration, neglecting the coupling dynamics between them. The current work examines the important rotordynamical behavior of coupled disk/shaft dynamics. A simplified nonlinear model is developed for lateral vibration of a rotor system with a bearing clearance nonlinearity. The steady-state dynamical behavior of this system is explored using numerical simulation and limit cycle analysis. It is demonstrated that bearing clearance effects can produce superharmonic vibration that may serve to excite high amplitude disk vibration. Such vibration could lead to significantly increased bearing loads and catastrophic failure of blades and disks. In addition, multi-valued responses and aperiodic behavior was observed.

Knaster-like continua and complex dynamics

1993 ◽  
Vol 13 (4) ◽  
pp. 627-634 ◽  
Author(s):  
Robert L. Devaney
Keyword(s):  
Complex Dynamics ◽  
Julia Set ◽  
Dynamical Behavior ◽  
Invariant Sets ◽  
Entire Plane ◽  
Limit Sets

AbstractIn this paper we discuss the topology and dynamics ofEλ(z) = λezwhen λ is real and λ > 1/e. It is known that the Julia set ofEλis the entire plane in this case. Our goal is to show that there are certain natural invariant subsets forEλwhich are topologically Knaster-like continua. Moreover, the dynamical behavior on these invariant sets is quite tame. We show that the only trivial kinds of α- and ω-limit sets are possible.

COMPLEX DYNAMICS IN COUPLED NONLINEAR ELEMENT SYSTEMS

1991 ◽  
Vol 05 (08) ◽  
pp. 1179-1214 ◽  
Author(s):  
KENJU OTSUKA
Keyword(s):  
Nonlinear Oscillator ◽  
Complex Dynamics ◽  
Landau Equation ◽  
Computer Experiments ◽  
Time Dependent ◽  
Chain Model ◽  
Ginzburg Landau ◽  
Physical Systems ◽  
Local Attractors ◽  
Discrete Complex

This paper reviews complex dynamics which arise through the interaction of simple nonlinear elements without chaotic response, including self-induced switching among local attractors (chaotic itinerancy) and related phenomena. Several realistic physical systems consisting of coupled nonlinear elements are considered on the basis of computer experiments: coupled nonlinear oscillator (e.g., discrete complex time-dependent Ginzburg-Landau equation) systems, coupled laser arrays, and a coupled multistable optical chain model.

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