284,617 research outputs found
Synchronization of fractional order chaotic systems
The chaotic dynamics of fractional order systems begin to attract much
attentions in recent years. In this brief report, we study the master-slave
synchronization of fractional order chaotic systems. It is shown that
fractional order chaotic systems can also be synchronized.Comment: 3 pages, 5 figure
Amplitude death in coupled chaotic oscillators
Amplitude death can occur in chaotic dynamical systems with time-delay
coupling, similar to the case of coupled limit cycles. The coupling leads to
stabilization of fixed points of the subsystems. This phenomenon is quite
general, and occurs for identical as well as nonidentical coupled chaotic
systems. Using the Lorenz and R\"ossler chaotic oscillators to construct
representative systems, various possible transitions from chaotic dynamics to
fixed points are discussed.Comment: To be published in PR
Mode fluctuations as fingerprint of chaotic and non-chaotic systems
The mode-fluctuation distribution is studied for chaotic as well as
for non-chaotic quantum billiards. This statistic is discussed in the broader
framework of the functions being the probability of finding energy
levels in a randomly chosen interval of length , and the distribution of
, where is the number of levels in such an interval, and their
cumulants . It is demonstrated that the cumulants provide a possible
measure for the distinction between chaotic and non-chaotic systems. The
vanishing of the normalized cumulants , , implies a Gaussian
behaviour of , which is realized in the case of chaotic systems, whereas
non-chaotic systems display non-vanishing values for these cumulants leading to
a non-Gaussian behaviour of . For some integrable systems there exist
rigorous proofs of the non-Gaussian behaviour which are also discussed. Our
numerical results and the rigorous results for integrable systems suggest that
a clear fingerprint of chaotic systems is provided by a Gaussian distribution
of the mode-fluctuation distribution .Comment: 44 pages, Postscript. The figures are included in low resolution
only. A full version is available at
http://www.physik.uni-ulm.de/theo/qc/baecker.htm
Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks
We study projective-anticipating, projective, and projective-lag
synchronization of time-delayed chaotic systems on random networks. We relax
some limitations of previous work, where projective-anticipating and
projective-lag synchronization can be achieved only on two coupled chaotic
systems. In this paper, we can realize projective-anticipating and
projective-lag synchronization on complex dynamical networks composed by a
large number of interconnected components. At the same time, although previous
work studied projective synchronization on complex dynamical networks, the
dynamics of the nodes are coupled partially linear chaotic systems. In this
paper, the dynamics of the nodes of the complex networks are time-delayed
chaotic systems without the limitation of the partial-linearity. Based on the
Lyapunov stability theory, we suggest a generic method to achieve the
projective-anticipating, projective, and projective-lag synchronization of
time-delayed chaotic systems on random dynamical networks and find both the
existence and sufficient stability conditions. The validity of the proposed
method is demonstrated and verified by examining specific examples using Ikeda
and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure
Spectral Statistics: From Disordered to Chaotic Systems
The relation between disordered and chaotic systems is investigated. It is
obtained by identifying the diffusion operator of the disordered systems with
the Perron-Frobenius operator in the general case. This association enables us
to extend results obtained in the diffusive regime to general chaotic systems.
In particular, the two--point level density correlator and the structure factor
for general chaotic systems are calculated and characterized. The behavior of
the structure factor around the Heisenberg time is quantitatively described in
terms of short periodic orbits.Comment: uuencoded file with 1 eps figure, 4 page
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