1,088 research outputs found
Scale-Free topologies and Activatory-Inhibitory interactions
A simple model of activatory-inhibitory interactions controlling the activity
of agents (substrates) through a "saturated response" dynamical rule in a
scale-free network is thoroughly studied. After discussing the most remarkable
dynamical features of the model, namely fragmentation and multistability, we
present a characterization of the temporal (periodic and chaotic) fluctuations
of the quasi-stasis asymptotic states of network activity. The double (both
structural and dynamical) source of entangled complexity of the system temporal
fluctuations, as an important partial aspect of the Correlation
Structure-Function problem, is further discussed to the light of the numerical
results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major
revision and new results incorporated. To appear in Chaos (2006
Exploring quantum chaos with a single nuclear spin
Most classical dynamical systems are chaotic. The trajectories of two
identical systems prepared in infinitesimally different initial conditions
diverge exponentially with time. Quantum systems, instead, exhibit
quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of
quantum systems whose classical counterparts are chaotic are expected to show
some features that resemble chaotic motion. Among the many controversial
aspects of the quantum-classical boundary, the emergence of chaos remains among
the least experimentally verified. Time-resolved observations of quantum
chaotic dynamics are particularly rare, and as yet unachieved in a single
particle, where the subtle interplay between chaos and quantum measurement
could be explored at its deepest levels. We present here a realistic proposal
to construct a chaotic driven top from the nuclear spin of a single donor atom
in silicon, in the presence of a nuclear quadrupole interaction. This system is
exquisitely measurable and controllable, and possesses extremely long intrinsic
quantum coherence times, allowing for the observation of subtle dynamical
behavior over extended periods. We show that signatures of chaos are expected
to arise for experimentally realizable parameters of the system, allowing the
study of the relation between quantum decoherence and classical chaos, and the
observation of dynamical tunneling.Comment: revised and published versio
Mutual synchronization and clustering in randomly coupled chaotic dynamical networks
We introduce and study systems of randomly coupled maps (RCM) where the
relevant parameter is the degree of connectivity in the system. Global
(almost-) synchronized states are found (equivalent to the synchronization
observed in globally coupled maps) until a certain critical threshold for the
connectivity is reached. We further show that not only the average
connectivity, but also the architecture of the couplings is responsible for the
cluster structure observed. We analyse the different phases of the system and
use various correlation measures in order to detect ordered non-synchronized
states. Finally, it is shown that the system displays a dynamical hierarchical
clustering which allows the definition of emerging graphs.Comment: 13 pages, to appear in Phys. Rev.
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