87 research outputs found
Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality
We discuss the role played by the Lyapunov exponents in the dynamics of
Zhang's model of Self-Organized Criticality. We show that a large part of the
spectrum (slowest modes) is associated with the energy transpor in the lattice.
In particular, we give bounds on the first negative Lyapunov exponent in terms
of the energy flux dissipated at the boundaries per unit of time. We then
establish an explicit formula for the transport modes that appear as diffusion
modes in a landscape where the metric is given by the density of active sites.
We use a finite size scaling ansatz for the Lyapunov spectrum and relate the
scaling exponent to the scaling of quantities like avalanche size, duration,
density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear
A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series
We describe methods of estimating the entire Lyapunov spectrum of a spatially
extended system from multivariate time-series observations. Provided that the
coupling in the system is short range, the Jacobian has a banded structure and
can be estimated using spatially localised reconstructions in low embedding
dimensions. This circumvents the ``curse of dimensionality'' that prevents the
accurate reconstruction of high-dimensional dynamics from observed time series.
The technique is illustrated using coupled map lattices as prototype models for
spatio-temporal chaos and is found to work even when the coupling is not
strictly local but only exponentially decaying.Comment: 13 pages, LaTeX (RevTeX), 13 Postscript figs, to be submitted to
Phys.Rev.
A hyperchaotic system without equilibrium
Abstract: This article introduces a new chaotic system of 4-D autonomous ordinary differential equations, which has no equilibrium. This system shows a hyper-chaotic attractor. There is no sink in this system as there is no equilibrium. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. There is little difference between this chaotic system and other chaotic systems with one or several equilibria shown by phase portraits, Lyapunov exponents and time series methods, but the Poincaré maps show this system is a chaotic system with more complicated dynamics. Moreover, the circuit realization is also presented
Histologic effects of mandibular protrusion splints in antigen-induced TMJ arthritis in rabbits
Contemporary management of TMJ involvement in JIA patients and its orofacial consequences
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