Chaos in time and space

Large-deviation approach to space-time chaos.

In this Letter, we show that the analysis of Lyapunov-exponent fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a gaussian approximation for the large-deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix D (a dynamical invariant itself) is measured and analyzed in terms of its principal ...

Space-Time Approach to Quantum Chaos

Universal scaling of Lyapunov-exponent fluctuations in space-time chaos.

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase space. A recent numerical study of spatially extended systems has revealed that the diffusion coefficient D of the Lyapunov exponents (LEs) exhibits a nontrivial scaling behavior, D(L)~L(-γ), with the system size L. He...

Scaling properties of growing noninfinitesimal perturbations in space-time chaos.

We study the spatiotemporal dynamics of random spatially distributed noninfinitesimal perturbations in one-dimensional chaotic extended systems. We find that an initial perturbation of finite size epsilon0 grows in time obeying the tangent space dynamic equations (Lyapunov vectors) up to a characteristic time tx(epsilon0) approximately b-(1/lambda(max))ln(epsilon0), where lambda(max) is the lar...

Critical properties of the synchronization transition in space-time chaos.

We study two coupled spatially extended dynamical systems which exhibit space-time chaos. The transition to the synchronized state is treated as a nonequilibrium phase transition, where the average synchronization error is the order parameter. The transition in one-dimensional systems is found to be generically in the universality class of the Kardar-Parisi-Zhang equation with a growth-limiting...