356 research outputs found
Strange Nonchaotic Attractors
Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic
attractors (SNAs). Such attractors are generic in quasiperiodically driven
nonlinear systems, and like strange attractors, are geometrically fractal. The
largest Lyapunov exponent is zero or negative: trajectories do not show
exponential sensitivity to initial conditions. In recent years, SNAs have been
seen in a number of diverse experimental situations ranging from
quasiperiodically driven mechanical or electronic systems to plasma discharges.
An important connection is the equivalence between a quasiperiodically driven
system and the Schr\"odinger equation for a particle in a related quasiperiodic
potential, giving a correspondence between the localized states of the quantum
problem with SNAs in the related dynamical system. In this review we discuss
the main conceptual issues in the study of SNAs, including the different
bifurcations or routes for the creation of such attractors, the methods of
characterization, and the nature of dynamical transitions in quasiperiodically
forced systems. The variation of the Lyapunov exponent, and the qualitative and
quantitative aspects of its local fluctuation properties, has emerged as an
important means of studying fractal attractors, and this analysis finds useful
application here. The ubiquity of such attractors, in conjunction with their
several unusual properties, suggest novel applications.Comment: 34 pages, 9 figures(5 figures are in ps format and four figures are
in gif format
Bifurcations and transitions in the quasiperiodically driven logistic map
We discuss several bifurcation phenomena that occur in the quasiperiodically
driven logistic map. This system can have strange nonchaotic attractors (SNAs)
in addition to chaotic and regular attractors; on SNAs the dynamics is
aperiodic, but the largest Lyapunov exponent is nonpositive. There are a number
of different transitions that occur here, from periodic attractors to SNAs,
from SNAs to chaotic attractors, etc. We describe some of these transitions by
examining the behavior of the largest Lyapunov exponent, distributions of
finite time Lyapunov exponents and the invariant densities in the phase space.Comment: 17 Pages, 8 Figures(four figures are in ps format and four figures
are in gif forma
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