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