13,512 research outputs found
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
Cluster synchronization in networks of coupled non-identical dynamical systems
In this paper, we study cluster synchronization in networks of coupled
non-identical dynamical systems. The vertices in the same cluster have the same
dynamics of uncoupled node system but the uncoupled node systems in different
clusters are different. We present conditions guaranteeing cluster
synchronization and investigate the relation between cluster synchronization
and the unweighted graph topology. We indicate that two condition play key
roles for cluster synchronization: the common inter-cluster coupling condition
and the intra-cluster communication. From the latter one, we interpret the two
well-known cluster synchronization schemes: self-organization and driving, by
whether the edges of communication paths lie at inter or intra-cluster. By this
way, we classify clusters according to whether the set of edges inter- or
intra-cluster edges are removable if wanting to keep the communication between
pairs of vertices in the same cluster. Also, we propose adaptive feedback
algorithms on the weights of the underlying graph, which can synchronize any
bi-directed networks satisfying the two conditions above. We also give several
numerical examples to illustrate the theoretical results
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators
We describe a flexible and modular delayed-feedback nonlinear oscillator that
is capable of generating a wide range of dynamical behaviours, from periodic
oscillations to high-dimensional chaos. The oscillator uses electrooptic
modulation and fibre-optic transmission, with feedback and filtering
implemented through real-time digital-signal processing. We consider two such
oscillators that are coupled to one another, and we identify the conditions
under which they will synchronize. By examining the rates of divergence or
convergence between two coupled oscillators, we quantify the maximum Lyapunov
exponents or transverse Lyapunov exponents of the system, and we present an
experimental method to determine these rates that does not require a
mathematical model of the system. Finally, we demonstrate a new adaptive
control method that keeps two oscillators synchronized even when the coupling
between them is changing unpredictably.Comment: 24 pages, 13 figures. To appear in Phil. Trans. R. Soc. A (special
theme issue to accompany 2009 International Workshop on Delayed Complex
Systems
Mathematical problems for complex networks
Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy
is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
Transmission of Information in Active Networks
Shannon's Capacity Theorem is the main concept behind the Theory of
Communication. It says that if the amount of information contained in a signal
is smaller than the channel capacity of a physical media of communication, it
can be transmitted with arbitrarily small probability of error. This theorem is
usually applicable to ideal channels of communication in which the information
to be transmitted does not alter the passive characteristics of the channel
that basically tries to reproduce the source of information. For an {\it active
channel}, a network formed by elements that are dynamical systems (such as
neurons, chaotic or periodic oscillators), it is unclear if such theorem is
applicable, once an active channel can adapt to the input of a signal, altering
its capacity. To shed light into this matter, we show, among other results, how
to calculate the information capacity of an active channel of communication.
Then, we show that the {\it channel capacity} depends on whether the active
channel is self-excitable or not and that, contrary to a current belief,
desynchronization can provide an environment in which large amounts of
information can be transmitted in a channel that is self-excitable. An
interesting case of a self-excitable active channel is a network of
electrically connected Hindmarsh-Rose chaotic neurons.Comment: 15 pages, 5 figures. submitted for publication. to appear in Phys.
Rev.
Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Nonreciprocal Channels
In this paper we propose and analyze a distributed algorithm for achieving
globally optimal decisions, either estimation or detection, through a
self-synchronization mechanism among linearly coupled integrators initialized
with local measurements. We model the interaction among the nodes as a directed
graph with weights dependent on the radio interface and we pose special
attention to the effect of the propagation delays occurring in the exchange of
data among sensors, as a function of the network geometry. We derive necessary
and sufficient conditions for the proposed system to reach a consensus on
globally optimal decision statistics. One of the major results proved in this
work is that a consensus is achieved for any bounded delay condition if and
only if the directed graph is quasi-strongly connected. We also provide a
closed form expression for the global consensus, showing that the effect of
delays is, in general, to introduce a bias in the final decision. The closed
form expression is also useful to modify the consensus mechanism in order to
get rid of the bias with minimum extra complexity.Comment: Conference paper. Journal version submitted to IEEE Transactions on
Signal Processing, January 10, 2007. Paper accepted for the publication on
the VIII IEEE Workshop on Signal Processing Advances in Wireless
Communications, (SPAWC 2007), January 22, 200
Global convergence of quorum-sensing networks
In many natural synchronization phenomena, communication between individual
elements occurs not directly, but rather through the environment. One of these
instances is bacterial quorum sensing, where bacteria release signaling
molecules in the environment which in turn are sensed and used for population
coordination. Extending this motivation to a general non- linear dynamical
system context, this paper analyzes synchronization phenomena in networks where
communication and coupling between nodes are mediated by shared dynamical quan-
tities, typically provided by the nodes' environment. Our model includes the
case when the dynamics of the shared variables themselves cannot be neglected
or indeed play a central part. Applications to examples from systems biology
illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages:
36
Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey
This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
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