Instabilities and fronts in extended systems

@inproceedings{Collet1990InstabilitiesAF,
  title={Instabilities and fronts in extended systems},
  author={P. Collet and Jean-Pierre Eckmann and Klaus Kirchg{\"a}ssner},
  year={1990}
}
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results often seem somewhat ad hoc, and it is not clear how to generalize them to the nextthat is, not yet solvedproblem. In an introduction to the subject of… 
Global Bifurcations and Chaotic Dynamics in Physical Applications
The aim of this work has been to analyse global bifurcations arising in a laser with injected signal and in a catalytic reaction on a surface of Pt, from the point of view of dynamical systems
Nonlinear convective instability of fronts: a case study
We consider a model system, consisting of two nonlinearly coupled partial differential equations, to investigate nonlinear convective instabilities of travelling waves. The system exhibits front
Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation
Abstract: We consider front solutions of the Swift–Hohenberg equation ∂tu= -(1+ ∂x2)2u + ɛ2u -u3. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using
Asymptotic stability and modulation of periodic wavetrains
The present memoir reports on recent investigations of the author and his collaborators on stability of periodic wavetrains. It includes answers to the last general questions concerning their
Attractors for modulation equations on unbounded domains-existence and comparison
We are interested in the long-time behaviour of nonlinear parabolic PDEs defined on unbounded cylindrical domains. For dissipative systems defined on bounded domains, the longtime behaviour can often
BISTABLE CML : EXISTENCE AND STABILITY OF FRONTS
We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatiotemporal coding, we prove the one-to-one
...
1
2
3
4
5
...