Terminating transient chaos in spatially extended systems

Chaos in Spatially Extended Systems via the Peak-Crossing bifurcation

Individual sites in spatially extended systems of coupled identical maps may exhibit chaotic behavior even if their intrinsic (local) dynamics is regular and stable. For this to happen it is imperative that the spatial interactions are sufficiently strong. So far, this scenario of generating chaos from simple local dynamics has been established rigorously only for special, very narrow classes o...

Transient dynamics and nonlinear stability of spatially extended systems.

As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilizat...

Entropy Production in Driven Spatially Extended Systems

This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production can be identified with a logarithmic ratio of microstate multiplicities of the original macrostate with respect to the time-reversed state. A special role is t...

Finite Propagation Speeds in Spatially Extended Systems

Rogue Waves in Spatially Extended Optical Systems

Giant anomalous events may occur in systems characterized by many waves, with extremely high amplitude waves appearing with a probability much higher than expected for a random dynamics. Such rare, and giant, events are known to occur on the ocean surface and have been named, in that context, “rogue waves”. We present here some recent experimental results on the statistical properties of giant ...