Introduction: dissipative localized structures in extended systems.

@article{Tlidi2007IntroductionDL,
  title={Introduction: dissipative localized structures in extended systems.},
  author={Mustapha Tlidi and Majid Taki and Theodore Kolokolnikov},
  journal={Chaos},
  year={2007},
  volume={17 3},
  pages={
          037101
        }
}
Localized structures belong to the class of dissipative structures found far from equilibrium. Contributions from the most representative groups working on a various fields of natural science such as biology, chemistry, plant ecology, mathematics, optics, and laser physics are presented. The aim of this issue is to gather specialists from these fields towards a cross-fertilization among these active areas of research and thereby to present an overview of the state of art in the formation and… 
View on PubMed
mathstat.dal.ca
55 Citations
Background Citations
7

55 Citations

Citation Type

Citation Type

Localized structures in dissipative media: from optics to plant ecology
TLDR
This Theme Issue contains contributions from 18 active groups involved in the LS field and have all made significant contributions in recent years.
Stationary localized structures and the effect of the delayed feedback in the Brusselator model
  • B. Kostet, M. Tlidi, +6 authors K. Panajotov
  • Mathematics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2018
TLDR
This paper investigates the formation of stationary localized structures in the Brusselator model and establishes a bifurcation diagram showing the emergence of localized spots, and incorporates delayed feedback control.
Effects of a localized beam on the dynamics of excitable cavity solitons
(Dated: August 19, 2008)We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerrmedium when a localized beam is applied on top of the homogeneous pumping. In…
Spontaneous motion of localized structures and localized patterns induced by delayed feedback
Abstract. We study the properties of 2D dissipative structures in a coherently driven optical resonator subjected to a delayed feedback. It has been predicted that delayed feedback can lead to the…
Strong nonlocal coupling stabilizes localized structures: an analysis based on front dynamics.
TLDR
An analytical formula is derived for the front interaction law and it is shown that the kinetics governing the formation of localized structures obeys a law inversely proportional to their size to some power.
Introduction to Focus Issue: Instabilities and nonequilibrium structures.
TLDR
This Focus Issue on instabilities and nonequilibrium structures includes invited contributions from leading researchers across many different fields and addresses a cross-disciplinary area of research as can be witnessed by the diversity of systems considered from inert matter such as photonics, chemistry, and fluid dynamics, to biology.
Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework.
TLDR
It is shown that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts.
Delayed feedback induces motion of localized spots in reaction-diffusion systems.
TLDR
It is shown that the delayed feedback induces a spontaneous motion of localized spots, characterized by computing analytically the velocity and the threshold above which localized structures start to move in an arbitrary direction.
Soliton lasers stabilized by coupling to a resonant linear system
Abstract Separation into spectral and nonlinear complex-eigenvalue problems is shown to be an effective and flexible approach to soliton laser models. The simplest such model, a complex…
Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons.
TLDR
It is observed that, in one case beams loose the radial symmetry while in the other one the radial symmetries are conserved during complicated beam transformations.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 19 REFERENCES
Dynamics of traveling pulses in heterogeneous media.
TLDR
It turns out that there are hidden ordered patterns associated with the critical points of ODEs that play a pivotal role in understanding the responses of the pulse; in fact, the depinning of pulses can be explained in terms of global bifurcations among those critical points.
Pattern formation in forced reaction diffusion systems with nearly degenerate bifurcations.
TLDR
It is shown that, when excitation occurs just after the Turing bifurcation and before the Hopf instability, the system exhibits a new type of stable standing-wave structures, namely the mixed-mode solutions.
Dissipative structures in left-handed material cavity optics.
TLDR
It is shown that the insertion of a left-handed material in an optical resonator allows for controlling the value and the sign of the diffraction coefficient in dispersive Kerr resonators and degenerate optical parametric oscillators.
Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes.
TLDR
Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes.
Homoclinic snaking: structure and stability.
The bistable Swift-Hohenberg equation exhibits multiple stable and unstable spatially localized states of arbitrary length in the vicinity of the Maxwell point between spatially homogeneous and…
Solitary pulses in linearly coupled Ginzburg-Landau equations.
TLDR
A brief review of dynamical models based on systems of linearly coupled complex Ginzburg-Landau (CGL) equations, including a model with quadratic (second-harmonic-generating) nonlinearity and a recently introduced model of a different but related type, based on linearly coupling CGL equations with cubic-quintic non linearity.
Classical solutions and pattern formation for a volume filling chemotaxis model.
TLDR
It is concluded that the emerging process of pattern formation is due to cell growth, and classical solutions to a generalized chemotaxis model, which includes the volume filling effect expressed through a nonlinear squeezing probability is established.
Interaction of dissipative Bragg solitons in active nonlinear fibers.
TLDR
A number of new phenomena are studied, including location of centers of motionless Solitons near the maxima of refractive index grating, the discreteness of moving solitons velocity and the existence of a motionless weakly coupled two-soliton structure.
Optical solitons as quantum objects.
TLDR
The rate of tunneling of classical bright solitons propagating in linearly coupled identical fibers is estimated by quantizing a simplified dynamics derived from the original Lagrangian equations with test functions, which could be within reach of the experiments, particularly if the quantum coherence of the soliton can be maintained over a sufficient time.
Stability of asymmetric spike solutions to the Gierer-Meinhardt system.
TLDR
It is confirmed that all such solutions are unstable in a neighborhood of the bifurcation point and an explicit expression for the leading order terms of the critical eigenvalues is derived.
...
1
2
...