1,882 research outputs found
A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays
Copyright @ 2012 Taylor & FrancisIn this article, the distributed consensus problem is considered for discrete-time delayed networks of dynamic agents with fixed topologies, where the networks under investigation are directed and the time-delays involved are distributed time delays including a single or multiple time delay(s) as special cases. By using the invariance principle of delay difference systems, a new unified framework is established to deal with the consensus for the discrete-time delayed multi-agent system. It is shown that the addressed discrete-time network with arbitrary distributed time delays reaches consensus provided that it is strongly connected. A numerical example is presented to illustrate the proposed methods.This work was supported in part by City University of Hong Kong under Grant 7008114, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 60774073 and 61074129, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2010313
Dynamic Topology Adaptation Based on Adaptive Link Selection Algorithms for Distributed Estimation
This paper presents adaptive link selection algorithms for distributed
estimation and considers their application to wireless sensor networks and
smart grids. In particular, exhaustive search--based
least--mean--squares(LMS)/recursive least squares(RLS) link selection
algorithms and sparsity--inspired LMS/RLS link selection algorithms that can
exploit the topology of networks with poor--quality links are considered. The
proposed link selection algorithms are then analyzed in terms of their
stability, steady--state and tracking performance, and computational
complexity. In comparison with existing centralized or distributed estimation
strategies, key features of the proposed algorithms are: 1) more accurate
estimates and faster convergence speed can be obtained; and 2) the network is
equipped with the ability of link selection that can circumvent link failures
and improve the estimation performance. The performance of the proposed
algorithms for distributed estimation is illustrated via simulations in
applications of wireless sensor networks and smart grids.Comment: 14 figure
Local/global analysis of the stationary solutions of some neural field equations
Neural or cortical fields are continuous assemblies of mesoscopic models,
also called neural masses, of neural populations that are fundamental in the
modeling of macroscopic parts of the brain. Neural fields are described by
nonlinear integro-differential equations. The solutions of these equations
represent the state of activity of these populations when submitted to inputs
from neighbouring brain areas. Understanding the properties of these solutions
is essential in advancing our understanding of the brain. In this paper we
study the dependency of the stationary solutions of the neural fields equations
with respect to the stiffness of the nonlinearity and the contrast of the
external inputs. This is done by using degree theory and bifurcation theory in
the context of functional, in particular infinite dimensional, spaces. The
joint use of these two theories allows us to make new detailed predictions
about the global and local behaviours of the solutions. We also provide a
generic finite dimensional approximation of these equations which allows us to
study in great details two models. The first model is a neural mass model of a
cortical hypercolumn of orientation sensitive neurons, the ring model. The
second model is a general neural field model where the spatial connectivity
isdescribed by heterogeneous Gaussian-like functions.Comment: 38 pages, 9 figure
Modeling phase synchronization of interacting neuronal populations:from phase reductions to collective behavior of oscillatory neural networks
Synchronous, coherent interaction is key for the functioning of our brain. The coordinated interplay between neurons and neural circuits allows to perceive, process and transmit information in the brain. As such, synchronization phenomena occur across all scales. The coordination of oscillatory activity between cortical regions is hypothesized to underlie the concept of phase synchronization. Accordingly, phase models have found their way into neuroscience. The concepts of neural synchrony and oscillations are introduced in Chapter 1 and linked to phase synchronization phenomena in oscillatory neural networks. Chapter 2 provides the necessary mathematical theory upon which a sound phase description builds. I outline phase reduction techniques to distill the phase dynamics from complex oscillatory networks. In Chapter 3 I apply them to networks of weakly coupled Brusselators and of Wilson-Cowan neural masses. Numerical and analytical approaches are compared against each other and their sensitivity to parameter regions and nonlinear coupling schemes is analysed. In Chapters 4 and 5 I investigate synchronization phenomena of complex phase oscillator networks. First, I study the effects of network-network interactions on the macroscopic dynamics when coupling two symmetric populations of phase oscillators. This setup is compared against a single network of oscillators whose frequencies are distributed according to a symmetric bimodal Lorentzian. Subsequently, I extend the applicability of the Ott-Antonsen ansatz to parameterdependent oscillatory systems. This allows for capturing the collective dynamics of coupled oscillators when additional parameters influence the individual dynamics. Chapter 6 draws the line to experimental data. The phase time series of resting state MEG data display large-scale brain activity at the edge of criticality. After reducing neurophysiological phase models from the underlying dynamics of Wilson-Cowan and Freeman neural masses, they are analyzed with respect to two complementary notions of critical dynamics. A general discussion and an outlook of future work are provided in the final Chapter 7
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