10,876 research outputs found
Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli
The collective dynamics of coupled two-dimensional chaotic maps on complex
networks is known to exhibit a rich variety of emergent properties which
crucially depend on the underlying network topology. We investigate the
collective motion of Chirikov standard maps interacting with time delay through
directed links of Gene Regulatory Network of bacterium Escherichia Coli.
Departures from strongly chaotic behavior of the isolated maps are studied in
relation to different coupling forms and strengths. At smaller coupling
intensities the network induces stable and coherent emergent dynamics. The
unstable behavior appearing with increase of coupling strength remains confined
within a connected sub-network. For the appropriate coupling, network exhibits
statistically robust self-organized dynamics in a weakly chaotic regime
Network analysis of chaotic dynamics in fixed-precision digital domain
When implemented in the digital domain with time, space and value discretized
in the binary form, many good dynamical properties of chaotic systems in
continuous domain may be degraded or even diminish. To measure the dynamic
complexity of a digital chaotic system, the dynamics can be transformed to the
form of a state-mapping network. Then, the parameters of the network are
verified by some typical dynamical metrics of the original chaotic system in
infinite precision, such as Lyapunov exponent and entropy. This article reviews
some representative works on the network-based analysis of digital chaotic
dynamics and presents a general framework for such analysis, unveiling some
intrinsic relationships between digital chaos and complex networks. As an
example for discussion, the dynamics of a state-mapping network of the Logistic
map in a fixed-precision computer is analyzed and discussed.Comment: 5 pages, 9 figure
Michaelis-Menten Dynamics in Complex Heterogeneous Networks
Biological networks have been recently found to exhibit many topological
properties of the so-called complex networks. It has been reported that they
are, in general, both highly skewed and directed. In this paper, we report on
the dynamics of a Michaelis-Menten like model when the topological features of
the underlying network resemble those of real biological networks.
Specifically, instead of using a random graph topology, we deal with a complex
heterogeneous network characterized by a power-law degree distribution coupled
to a continuous dynamics for each network's component. The dynamics of the
model is very rich and stationary, periodic and chaotic states are observed
upon variation of the model's parameters. We characterize these states
numerically and report on several quantities such as the system's phase diagram
and size distributions of clusters of stationary, periodic and chaotic nodes.
The results are discussed in view of recent debate about the ubiquity of
complex networks in nature and on the basis of several biological processes
that can be well described by the dynamics studied.Comment: Paper enlarged and modified, including the title. Some problems with
the pdf were detected in the past. If they persist, please ask for the pdf by
e-mailing yamir(at_no_spam)unizar.es. Version to appear in Physica
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
Lagrangian Flow Network approach to an open flow model
Concepts and tools from network theory, the so-called Lagrangian Flow Network
framework, have been successfully used to obtain a coarse-grained description
of transport by closed fluid flows. Here we explore the application of this
methodology to open chaotic flows, and check it with numerical results for a
model open flow, namely a jet with a localized wave perturbation. We find that
network nodes with high values of out-degree and of finite-time entropy in the
forward-in-time direction identify the location of the chaotic saddle and its
stable manifold, whereas nodes with high in-degree and backwards finite-time
entropy highlight the location of the saddle and its unstable manifold. The
cyclic clustering coefficient, associated to the presence of periodic orbits,
takes non-vanishing values at the location of the saddle itself.Comment: 7 pages, 3 figures. To appear in European Physical Journal Special
Topics, Topical Issue on "Recent Advances in Nonlinear Dynamics and Complex
Structures: Fundamentals and Applications
Pinning Complex Networks by a Single Controller
In this paper, without assuming symmetry, irreducibility, or linearity of the
couplings, we prove that a single controller can pin a coupled complex network
to a homogenous solution. Sufficient conditions are presented to guarantee the
convergence of the pinning process locally and globally. An effective approach
to adapt the coupling strength is proposed. Several numerical simulations are
given to verify our theoretical analysis
Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
We investigate a generalised version of the recently proposed ordinal
partition time series to network transformation algorithm. Firstly we introduce
a fixed time lag for the elements of each partition that is selected using
techniques from traditional time delay embedding. The resulting partitions
define regions in the embedding phase space that are mapped to nodes in the
network space. Edges are allocated between nodes based on temporal succession
thus creating a Markov chain representation of the time series. We then apply
this new transformation algorithm to time series generated by the R\"ossler
system and find that periodic dynamics translate to ring structures whereas
chaotic time series translate to band or tube-like structures -- thereby
indicating that our algorithm generates networks whose structure is sensitive
to system dynamics. Furthermore we demonstrate that simple network measures
including the mean out degree and variance of out degrees can track changes in
the dynamical behaviour in a manner comparable to the largest Lyapunov
exponent. We also apply the same analysis to experimental time series generated
by a diode resonator circuit and show that the network size, mean shortest path
length and network diameter are highly sensitive to the interior crisis
captured in this particular data set
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