18 research outputs found
Discrete chaotic states of a Bose-Einstein condensate
We find the different spatial chaos in a one-dimensional attractive
Bose-Einstein condensate interacting with a Gaussian-like laser barrier and
perturbed by a weak optical lattice. For the low laser barrier the chaotic
regions of parameters are demonstrated and the chaotic and regular states are
illustrated numerically. In the high barrier case, the bounded perturbed
solutions which describe a set of discrete chaotic states are constructed for
the discrete barrier heights and magic numbers of condensed atoms. The chaotic
density profiles are exhibited numerically for the lowest quantum number, and
the analytically bounded but numerically unbounded Gaussian-like configurations
are confirmed. It is shown that the chaotic wave packets can be controlled
experimentally by adjusting the laser barrier potential.Comment: 7 pages, 5 figure
Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum
We study bifurcations associated with stability of the lowest stationary
point (SP) of a damped parametrically forced pendulum by varying
(the natural frequency of the pendulum) and (the amplitude of the external
driving force). As is increased, the SP will restabilize after its
instability, destabilize again, and so {\it ad infinitum} for any given
. Its destabilizations (restabilizations) occur via alternating
supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork
bifurcations, except the first destabilization at which a supercritical or
subcritical bifurcation takes place depending on the value of . For
each case of the supercritical destabilizations, an infinite sequence of PDB's
follows and leads to chaos. Consequently, an infinite series of period-doubling
transitions to chaos appears with increasing . The critical behaviors at the
transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.
Period p-tuplings in coupled maps
We study the critical behavior (CB) of all period -tuplings in symmetrically coupled
one-dimensional maps. We first investigate the CB for the case of two
coupled maps, using a renormalization method. Three (five) kinds of fixed
points of the renormalization transformation and their relevant ``coupling
eigenvalues'' associated with coupling perturbations are found in the case of
even (odd) . We next study the CB for the linear- and nonlinear-coupling
cases (a coupling is called linear or nonlinear according to its leading term),
and confirm the renormalization results. Both the structure of the critical set
(set of the critical points) and the CB vary according as the coupling is
linear or nonlinear. Finally, the results of the two coupled maps are extended
to many coupled maps with , in which the CB depends on the range of
coupling.Comment: RevTeX, 30 figures available upon reques