8,653 research outputs found
Asynchronous Networks and Event Driven Dynamics
Real-world networks in technology, engineering and biology often exhibit
dynamics that cannot be adequately reproduced using network models given by
smooth dynamical systems and a fixed network topology. Asynchronous networks
give a theoretical and conceptual framework for the study of network dynamics
where nodes can evolve independently of one another, be constrained, stop, and
later restart, and where the interaction between different components of the
network may depend on time, state, and stochastic effects. This framework is
sufficiently general to encompass a wide range of applications ranging from
engineering to neuroscience. Typically, dynamics is piecewise smooth and there
are relationships with Filippov systems. In the first part of the paper, we
give examples of asynchronous networks, and describe the basic formalism and
structure. In the second part, we make the notion of a functional asynchronous
network rigorous, discuss the phenomenon of dynamical locks, and present a
foundational result on the spatiotemporal factorization of the dynamics for a
large class of functional asynchronous networks
Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays
This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, 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
The brainstem reticular formation is a small-world, not scale-free, network
Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement
Symmetries, Stability, and Control in Nonlinear Systems and Networks
This paper discusses the interplay of symmetries and stability in the
analysis and control of nonlinear dynamical systems and networks. Specifically,
it combines standard results on symmetries and equivariance with recent
convergence analysis tools based on nonlinear contraction theory and virtual
dynamical systems. This synergy between structural properties (symmetries) and
convergence properties (contraction) is illustrated in the contexts of network
motifs arising e.g. in genetic networks, of invariance to environmental
symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio
A Low Dimensional Description of Globally Coupled Heterogeneous Neural Networks of Excitatory and Inhibitory Neurons
Neural networks consisting of globally coupled excitatory and inhibitory nonidentical neurons may exhibit a complex dynamic behavior including synchronization, multiclustered solutions in phase space, and oscillator death. We investigate the conditions under which these behaviors occur in a multidimensional parametric space defined by the connectivity strengths and dispersion of the neuronal membrane excitability. Using mode decomposition techniques, we further derive analytically a low dimensional description of the neural population dynamics and show that the various dynamic behaviors of the entire network can be well reproduced by this reduced system. Examples of networks of FitzHugh-Nagumo and Hindmarsh-Rose neurons are discussed in detail
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
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