3,652 research outputs found
Symbolic dynamics and synchronization of coupled map networks with multiple delays
We use symbolic dynamics to study discrete-time dynamical systems with
multiple time delays. We exploit the concept of avoiding sets, which arise from
specific non-generating partitions of the phase space and restrict the
occurrence of certain symbol sequences related to the characteristics of the
dynamics. In particular, we show that the resulting forbidden sequences are
closely related to the time delays in the system. We present two applications
to coupled map lattices, namely (1) detecting synchronization and (2)
determining unknown values of the transmission delays in networks with possibly
directed and weighted connections and measurement noise. The method is
applicable to multi-dimensional as well as set-valued maps, and to networks
with time-varying delays and connection structure.Comment: 13 pages, 4 figure
The Origin of Non-chaotic Behavior in Identically Driven Systems
Recently it has been found that different physical systems driven by
identical random noise behave exactly identical after a long time. It is also
suggested that this is an outcome of finite precision in numerical experiments.
Here we show that the origin of the non-chaotic behavior lies in the structural
instability of the attractor of these systems which changes to a stable fixed
point for strong enough drive. We see this to be true in all the systems
studied in literature. Thus we affirm that in chaotic systems, synchronization
can not occur only by addition of noise unless the noise destroys the strange
attractor and the system is no longer chaotic.Comment: Figures could be obtained from [email protected]. The document
below is a latex fil
Void-induced cross slip of screw dislocations in fcc copper
Pinning interaction between a screw dislocation and a void in fcc copper is
investigated by means of molecular dynamics simulation. A screw dislocation
bows out to undergo depinning on the original glide plane at low temperatures,
where the behavior of the depinning stress is consistent with that obtained by
a continuum model. If the temperature is higher than 300 K, the motion of a
screw dislocation is no longer restricted to a single glide plane due to cross
slip on the void surface. Several depinning mechanisms that involve multiple
glide planes are found. In particular, a depinning mechanism that produces an
intrinsic prismatic loop is found. We show that these complex depinning
mechanisms significantly increase the depinning stress
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.
Inter-Intra Molecular Dynamics as an Iterated Function System
The dynamics of units (molecules) with slowly relaxing internal states is
studied as an iterated function system (IFS) for the situation common in e.g.
biological systems where these units are subjected to frequent collisional
interactions. It is found that an increase in the collision frequency leads to
successive discrete states that can be analyzed as partial steps to form a
Cantor set. By considering the interactions among the units, a self-consistent
IFS is derived, which leads to the formation and stabilization of multiple such
discrete states. The relevance of the results to dynamical multiple states in
biomolecules in crowded conditions is discussed.Comment: 7 pages, 7 figures. submitted to Europhysics Letter
Characterization of chaos in random maps
We discuss the characterization of chaotic behaviours in random maps both in
terms of the Lyapunov exponent and of the spectral properties of the
Perron-Frobenius operator. In particular, we study a logistic map where the
control parameter is extracted at random at each time step by considering
finite dimensional approximation of the Perron-Frobenius operatorComment: Plane TeX file, 15 pages, and 5 figures available under request to
[email protected]
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