4,718 research outputs found
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution
figures is available at http://www.pks.mpg.de/~edugal
A New Type of Irregular Motion in a Class of Game Dynamics Systems
A new type of asymptotic behavior in a game dynamics system is discovered.
The system exhibits behavior which combines chaotic motion and attraction to
heteroclinic cycles; the trajectory visits several unstable stationary states
repeatedly with an irregular order, and the typical length of the stay near the
steady states grows exponentially with the number of visits. The dynamics
underlying this irregular motion is analyzed by introducing a dynamically
rescaled time variable, and its relation to the low-dimensional chaotic
dynamics is thus uncovered. The relation of this irregular motion with a
strange type of instability of heteroclinic cycles is also examined.Comment: 7 pages (Revtex) + 4 figures (postscript
Cycle expansions for intermittent maps
In a generic dynamical system chaos and regular motion coexist side by side,
in different parts of the phase space. The border between these, where
trajectories are neither unstable nor stable but of marginal stability,
manifests itself through intermittency, dynamics where long periods of nearly
regular motions are interrupted by irregular chaotic bursts. We discuss the
Perron-Frobenius operator formalism for such systems, and show by means of a
1-dimensional intermittent map that intermittency induces branch cuts in
dynamical zeta functions. Marginality leads to long-time dynamical
correlations, in contrast to the exponentially fast decorrelations of purely
chaotic dynamics. We apply the periodic orbit theory to quantitative
characterization of the associated power-law decays.Comment: 22 pages, 5 figure
Delay time modulation induced oscillating synchronization and intermittent anticipatory/lag and complete synchronizations in time-delay nonlinear dynamical systems
Existence of a new type of oscillating synchronization that oscillates
between three different types of synchronizations (anticipatory, complete and
lag synchronizations) is identified in unidirectionally coupled nonlinear
time-delay systems having two different time-delays, that is feedback delay
with a periodic delay time modulation and a constant coupling delay.
Intermittent anticipatory, intermittent lag and complete synchronizations are
shown to exist in the same system with identical delay time modulations in both
the delays. The transition from anticipatory to complete synchronization and
from complete to lag synchronization as a function of coupling delay with
suitable stability condition is discussed. The intermittent anticipatory and
lag synchronizations are characterized by the minimum of similarity functions
and the intermittent behavior is characterized by a universal asymptotic
power law distribution. It is also shown that the delay time carved
out of the trajectories of the time-delay system with periodic delay time
modulation cannot be estimated using conventional methods, thereby reducing the
possibility of decoding the message by phase space reconstruction.Comment: accepted for publication in CHAOS, revised in response to referees
comment
Chaos in credit–constrained emerging economies with Leontief technology
This work provides a framework to analyze the role of financial development as a source of endogenous instability in emerging economies subject to moral hazard problems. We study a piecewise linear dynamic model describing a small open economy with a tradable good produced by internationally mobile capital and a country specific production factor, using Leontief technology. We demonstrate that emerging markets could be endogenously unstable when large capital in–flows increase risk and exacerbate asymmetric information problems, according to empirical evidence. Using bifurcation and stability analysis we describe the properties of the system attractors, we assess the plausibility for complex dynamics and we find out that border collision bifurcations can emerge.border collision bifurcations,,complex dynamics,,emerging economies,,CEECs,,Endogenous instability,,moral hazard,,piecewise linear map.
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