Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
Total Pages: 1885
Release: 2011-10-05
Genre: Mathematics
ISBN: 1461418054

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Dynamics Of Complex Systems

Dynamics Of Complex Systems
Author: Yaneer Bar-yam
Publisher: CRC Press
Total Pages: 866
Release: 2019-03-04
Genre: Mathematics
ISBN: 0429717598

This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.

Chaos and Dynamical Systems

Chaos and Dynamical Systems
Author: David P. Feldman
Publisher: Princeton University Press
Total Pages: 262
Release: 2019-08-06
Genre: Mathematics
ISBN: 0691161526

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Complex and Adaptive Dynamical Systems

Complex and Adaptive Dynamical Systems
Author: Claudius Gros
Publisher: Springer
Total Pages: 0
Release: 2015-04-14
Genre: Mathematics
ISBN: 9783319162645

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).

Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems

Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems
Author: M. Reza Rahimi Tabar
Publisher: Springer
Total Pages: 290
Release: 2019-07-04
Genre: Science
ISBN: 3030184722

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

Introduction to the Modern Theory of Dynamical Systems

Introduction to the Modern Theory of Dynamical Systems
Author: Anatole Katok
Publisher: Cambridge University Press
Total Pages: 828
Release: 1995
Genre: Mathematics
ISBN: 9780521575577

This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.

Dynamical Systems

Dynamical Systems
Author: Jürgen Jost
Publisher: Springer Science & Business Media
Total Pages: 199
Release: 2005-11-24
Genre: Science
ISBN: 3540288899

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

Dynamical Systems on Networks

Dynamical Systems on Networks
Author: Mason Porter
Publisher: Springer
Total Pages: 91
Release: 2016-03-31
Genre: Mathematics
ISBN: 3319266411

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.

Information Dynamics

Information Dynamics
Author: Harald Atmanspacher
Publisher: Springer Science & Business Media
Total Pages: 362
Release: 2013-11-11
Genre: Technology & Engineering
ISBN: 1489923055

Proceedings of a NATO ASI held in Irsee/Kaufbeuren, Germany, June 15--26, 1990