Dynamical Systems On Networks
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Dynamical Systems On Networks
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Author : Mason Porter
language : en
Publisher: Springer
Release Date : 2016-03-31
Dynamical Systems On Networks written by Mason Porter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-31 with Mathematics categories.
This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.
Synchronization In Complex Networks Of Nonlinear Dynamical Systems
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Author : Chai Wah Wu
language : en
Publisher: World Scientific
Release Date : 2007
Synchronization In Complex Networks Of Nonlinear Dynamical Systems written by Chai Wah Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.
Dynamical Processes On Complex Networks
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Author : Alain Barrat
language : en
Publisher: Cambridge University Press
Release Date : 2012-10-11
Dynamical Processes On Complex Networks written by Alain Barrat and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-11 with Science categories.
The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number of everyday systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This new and recent account presents a comprehensive explanation of these effects.
Complex And Adaptive Dynamical Systems
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Author : Claudius Gros
language : en
Publisher: Springer
Release Date : 2015-04-01
Complex And Adaptive Dynamical Systems written by Claudius Gros and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Science categories.
This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter includes exercises and suggestions for further reading, and the solutions to all exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teac hing and self-education. Very well structured and every topic is illustrated with simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009).
An Introduction To Sequential Dynamical Systems
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Author : Henning Mortveit
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-27
An Introduction To Sequential Dynamical Systems written by Henning Mortveit and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-27 with Mathematics categories.
This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.
Modelling Analysis And Control Of Networked Dynamical Systems
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Author : Ziyang Meng
language : en
Publisher: Springer Nature
Release Date : 2021-10-15
Modelling Analysis And Control Of Networked Dynamical Systems written by Ziyang Meng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-15 with Science categories.
This monograph provides a comprehensive exploration of new tools for modelling, analysis, and control of networked dynamical systems. Expanding on the authors’ previous work, this volume highlights how local exchange of information and cooperation among neighboring agents can lead to emergent global behaviors in a given networked dynamical system. Divided into four sections, the first part of the book begins with some preliminaries and the general networked dynamical model that is used throughout the rest of the book. The second part focuses on synchronization of networked dynamical systems, synchronization with non-expansive dynamics, periodic solutions of networked dynamical systems, and modulus consensus of cooperative-antagonistic networks. In the third section, the authors solve control problems with input constraint, large delays, and heterogeneous dynamics. The final section of the book is devoted to applications, studying control problems of spacecraft formation flying, multi-robot rendezvous, and energy resource coordination of power networks. Modelling, Analysis, and Control of Networked Dynamical Systems will appeal to researchers and graduate students interested in control theory and its applications, particularly those working in networked control systems, multi-agent systems, and cyber-physical systems. This volume can also be used in advanced undergraduate and graduate courses on networked control systems and multi-agent systems.
Dynamical Systems
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-24
Dynamical Systems written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-24 with Science categories.
Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata
Stability Of Dynamical Systems
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
Stability Of Dynamical Systems written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differentiable dynamical systems categories.
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
Discrete Time And Discrete Space Dynamical Systems
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Author : Kuize Zhang
language : en
Publisher: Springer
Release Date : 2019-08-06
Discrete Time And Discrete Space Dynamical Systems written by Kuize Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-06 with Technology & Engineering categories.
Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including: Boolean control networks; nondeterministic finite-transition systems; finite automata; labelled Petri nets; and cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology. Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.