106 research outputs found
Strange nonchaotic attractors in noise driven systems
Strange nonchaotic attractors (SNAs) in noise driven systems are
investigated. Before the transition to chaos, due to the effect of noise, a
typical trajectory will wander between the periodic attractor and its nearby
chaotic saddle in an intermittent way, forms a strange attractor gradually. The
existence of SNAs is confirmed by simulation results of various critera both in
map and continuous systems. Dimension transition is found and intermittent
behavior is studied by peoperties of local Lyapunov exponent. The universality
and generalization of this kind of SNAs are discussed and common features are
concluded
Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing
Large assemblies of nonlinear dynamical units driven by a long-wave
fluctuating external field are found to generate strong turbulence with scaling
properties. This type of turbulence is so robust that it persists over a finite
parameter range with parameter-dependent exponents of singularity, and is
insensitive to the specific nature of the dynamical units involved. Whether or
not the units are coupled with their neighborhood is also unimportant. It is
discovered numerically that the derivative of the field exhibits strong spatial
intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR
Small world effect in an epidemiological model
A model for the spread of an infection is analyzed for different population
structures. The interactions within the population are described by small world
networks, ranging from ordered lattices to random graphs. For the more ordered
systems, there is a fluctuating endemic state of low infection. At a finite
value of the disorder of the network, we find a transition to self-sustained
oscillations in the size of the infected subpopulation
Fractalization of Torus Revisited as a Strange Nonchaotic Attractor
Fractalization of torus and its transition to chaos in a quasi-periodically
forced logistic map is re-investigated in relation with a strange nonchaotic
attractor, with the aid of functional equation for the invariant curve.
Existence of fractal torus in an interval in parameter space is confirmed by
the length and the number of extrema of the torus attractor, as well as the
Fourier mode analysis. Mechanisms of the onset of fractal torus and the
transition to chaos are studied in connection with the intermittency.Comment: Latex file ( figures will be sent electronically upon
request):submitted to Phys.Rev. E (1996
Spectral Properties and Synchronization in Coupled Map Lattices
Spectral properties of Coupled Map Lattices are described. Conditions for the
stability of spatially homogeneous chaotic solutions are derived using linear
stability analysis. Global stability analysis results are also presented. The
analytical results are supplemented with numerical examples. The quadratic map
is used for the site dynamics with different coupling schemes such as global
coupling, nearest neighbor coupling, intermediate range coupling, random
coupling, small world coupling and scale free coupling.Comment: 10 pages with 15 figures (Postscript), REVTEX format. To appear in
PR
Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven Duffing oscillator
Different mechanisms for the creation of strange nonchaotic attractors (SNAs)
are studied in a two-frequency parametrically driven Duffing oscillator. We
focus on intermittency transitions in particular, and show that SNAs in this
system are created through quasiperiodic saddle-node bifurcations (Type-I
intermittency) as well as through a quasiperiodic subharmonic bifurcation
(Type-III intermittency). The intermittent attractors are characterized via a
number of Lyapunov measures including the behavior of the largest nontrivial
Lyapunov exponent and its variance as well as through distributions of
finite-time Lyapunov exponents. These attractors are ubiquitous in
quasiperiodically driven systems; the regions of occurrence of various SNAs are
identified in a phase diagram of the Duffing system.Comment: 24 pages, RevTeX 4, 12 EPS figure
Synchronization and directed percolation in coupled map lattices
We study a synchronization mechanism, based on one-way coupling of
all-or-nothing type, applied to coupled map lattices with several different
local rules. By analyzing the metric and the topological distance between the
two systems, we found two different regimes: a strong chaos phase in which the
transition has a directed percolation character and a weak chaos phase in which
the synchronization transition occurs abruptly. We are able to derive some
analytical approximations for the location of the transition point and the
critical properties of the system.
We propose to use the characteristics of this transition as indicators of the
spatial propagation of chaoticity.Comment: 12 pages + 12 figure
Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions
We consider the existence of robust strange nonchaotic attractors (SNA's) in
a simple class of quasiperiodically forced systems. Rigorous results are
presented demonstrating that the resulting attractors are strange in the sense
that their box-counting dimension is N+1 while their information dimension is
N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure
Superconducting states and depinning transitions of Josephson ladders
We present analytical and numerical studies of pinned superconducting states
of open-ended Josephson ladder arrays, neglecting inductances but taking edge
effects into account. Treating the edge effects perturbatively, we find
analytical approximations for three of these superconducting states -- the
no-vortex, fully-frustrated and single-vortex states -- as functions of the dc
bias current and the frustration . Bifurcation theory is used to derive
formulas for the depinning currents and critical frustrations at which the
superconducting states disappear or lose dynamical stability as and are
varied. These results are combined to yield a zero-temperature stability
diagram of the system with respect to and . To highlight the effects of
the edges, we compare this dynamical stability diagram to the thermodynamic
phase diagram for the infinite system where edges have been neglected. We
briefly indicate how to extend our methods to include self-inductances.Comment: RevTeX, 22 pages, 17 figures included; Errata added, 1 page, 1
corrected figur
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