1,983 research outputs found
Complex network analysis and nonlinear dynamics
This chapter aims at reviewing complex network and nonlinear dynamical
models and methods that were either developed for or applied to socioeconomic
issues, and pertinent to the theme of New Economic Geography. After an introduction
to the foundations of the field of complex networks, the present summary
introduces some applications of complex networks to economics, finance, epidemic
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issue
Coupled map gas: structure formation and dynamics of interacting motile elements with internal dynamics
A model of interacting motile chaotic elements is proposed. The chaotic
elements are distributed in space and interact with each other through
interactions depending on their positions and their internal states. As the
value of a governing parameter is changed, the model exhibits successive phase
changes with novel pattern dynamics, including spatial clustering, fusion and
fission of clusters and intermittent diffusion of elements. We explain the
manner in which the interplay between internal dynamics and interaction leads
to this behavior by employing certain quantities characterizing diffusion,
correlation, and the information cascade of synchronization. Keywords:
collective motion, coupled map system, interacting motile elementsComment: 27 pages, 12 figures; submitted to Physica
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Applied Koopman Operator Theory for Power Systems Technology
Koopman operator is a composition operator defined for a dynamical system
described by nonlinear differential or difference equation. Although the
original system is nonlinear and evolves on a finite-dimensional state space,
the Koopman operator itself is linear but infinite-dimensional (evolves on a
function space). This linear operator captures the full information of the
dynamics described by the original nonlinear system. In particular, spectral
properties of the Koopman operator play a crucial role in analyzing the
original system. In the first part of this paper, we review the so-called
Koopman operator theory for nonlinear dynamical systems, with emphasis on modal
decomposition and computation that are direct to wide applications. Then, in
the second part, we present a series of applications of the Koopman operator
theory to power systems technology. The applications are established as
data-centric methods, namely, how to use massive quantities of data obtained
numerically and experimentally, through spectral analysis of the Koopman
operator: coherency identification of swings in coupled synchronous generators,
precursor diagnostic of instabilities in the coupled swing dynamics, and
stability assessment of power systems without any use of mathematical models.
Future problems of this research direction are identified in the last
concluding part of this paper.Comment: 31 pages, 11 figure
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.
An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination
This article reviews some main results and progress in distributed
multi-agent coordination, focusing on papers published in major control systems
and robotics journals since 2006. Distributed coordination of multiple
vehicles, including unmanned aerial vehicles, unmanned ground vehicles and
unmanned underwater vehicles, has been a very active research subject studied
extensively by the systems and control community. The recent results in this
area are categorized into several directions, such as consensus, formation
control, optimization, task assignment, and estimation. After the review, a
short discussion section is included to summarize the existing research and to
propose several promising research directions along with some open problems
that are deemed important for further investigations
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