4,874 research outputs found
Symbolic Synchronization and the Detection of Global Properties of Coupled Dynamics from Local Information
We study coupled dynamics on networks using symbolic dynamics. The symbolic
dynamics is defined by dividing the state space into a small number of regions
(typically 2), and considering the relative frequencies of the transitions
between those regions. It turns out that the global qualitative properties of
the coupled dynamics can be classified into three different phases based on the
synchronization of the variables and the homogeneity of the symbolic dynamics.
Of particular interest is the {\it homogeneous unsynchronized phase} where the
coupled dynamics is in a chaotic unsynchronized state, but exhibits (almost)
identical symbolic dynamics at all the nodes in the network. We refer to this
dynamical behaviour as {\it symbolic synchronization}. In this phase, the local
symbolic dynamics of any arbitrarily selected node reflects global properties
of the coupled dynamics, such as qualitative behaviour of the largest Lyapunov
exponent and phase synchronization. This phase depends mainly on the network
architecture, and only to a smaller extent on the local chaotic dynamical
function. We present results for two model dynamics, iterations of the
one-dimensional logistic map and the two-dimensional H\'enon map, as local
dynamical function.Comment: 21 pages, 7 figure
Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
Coupled oscillators are shown to experience amplitude death for a much larger
set of parameter values when they are connected with time delays distributed
over an interval rather than concentrated at a point. Distributed delays
enlarge and merge death islands in the parameter space. Furthermore, when the
variance of the distribution is larger than a threshold the death region
becomes unbounded and amplitude death can occur for any average value of delay.
These phenomena are observed even with a small spread of delays, for different
distribution functions, and an arbitrary number of oscillators.Comment: 4 pages, 5 figure
MACROECONOMIC DETERMINANTS OF RADICAL INNOVATIONS AND INTERNET BANKING IN EUROPE
Current technological development has various implications for the bankingsector. Especially, the banks prefer internet banking to keep up their customers, reducetransaction costs, enhance their customers’ portfolio, and accelerate financial transactions.In this regard, this study aims at finding out the use of intensity of internet banking. Extensivetechnological innovation boosts internet banking. Banks use internet services as anaggressive business strategy to gain market share rather than for making profits. Theimportance of the innovation for the banking sector is that the competition forces banks to beinnovative in order to survive in the market. In the macroeconomic level, R&D expenditures,education expenditures, skilled human capital, level of the information and communicationinfrastructure and the accessing the internet by the individuals, patent protection laws, thelevel of the competition in national and international markets, the cost of inputs such asenergy or wages can affect the innovation.Radical Innovation, Internet Banking, Macroeconomy
Network synchronization: Spectral versus statistical properties
We consider synchronization of weighted networks, possibly with asymmetrical
connections. We show that the synchronizability of the networks cannot be
directly inferred from their statistical properties. Small local changes in the
network structure can sensitively affect the eigenvalues relevant for
synchronization, while the gross statistical network properties remain
essentially unchanged. Consequently, commonly used statistical properties,
including the degree distribution, degree homogeneity, average degree, average
distance, degree correlation, and clustering coefficient, can fail to
characterize the synchronizability of networks
Local pinning of networks of multi-agent systems with transmission and pinning delays
We study the stability of networks of multi-agent systems with local pinning
strategies and two types of time delays, namely the transmission delay in the
network and the pinning delay of the controllers. Sufficient conditions for
stability are derived under specific scenarios by computing or estimating the
dominant eigenvalue of the characteristic equation. In addition, controlling
the network by pinning a single node is studied. Moreover, perturbation methods
are employed to derive conditions in the limit of small and large pinning
strengths.Numerical algorithms are proposed to verify stability, and simulation
examples are presented to confirm the efficiency of analytic results.Comment: 6 pages, 3 figure
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
Complex transitions to synchronization in delay-coupled networks of logistic maps
A network of delay-coupled logistic maps exhibits two different
synchronization regimes, depending on the distribution of the coupling delay
times. When the delays are homogeneous throughout the network, the network
synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92,
144101 (2004)], which may be periodic or chaotic depending on the delay; when
the delays are sufficiently heterogeneous, the synchronization proceeds to a
steady-state, which is unstable for the uncoupled map [Masoller and Marti,
Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from
time-dependent to steady-state synchronization as the width of the delay
distribution increases. We also compare the two transitions to synchronization
as the coupling strength increases. We use transition probabilities calculated
via symbolic analysis and ordinal patterns. We find that, as the coupling
strength increases, before the onset of steady-state synchronization the
network splits into two clusters which are in anti-phase relation with each
other. On the other hand, with increasing delay heterogeneity, no cluster
formation is seen at the onset of steady-state synchronization; however, a
rather complex unsynchronized state is detected, revealed by a diversity of
transition probabilities in the network nodes
Synchronization in discrete-time networks with general pairwise coupling
We consider complete synchronization of identical maps coupled through a
general interaction function and in a general network topology where the edges
may be directed and may carry both positive and negative weights. We define
mixed transverse exponents and derive sufficient conditions for local complete
synchronization. The general non-diffusive coupling scheme can lead to new
synchronous behavior, in networks of identical units, that cannot be produced
by single units in isolation. In particular, we show that synchronous chaos can
emerge in networks of simple units. Conversely, in networks of chaotic units
simple synchronous dynamics can emerge; that is, chaos can be suppressed
through synchrony
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