Download or read book Chaotic Fractional and Complex Dynamics New Insights and Perspectives written by Mark Edelman and published by Springer. This book was released on 2017-11-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.
Download or read book Complex and Adaptive Dynamical Systems written by Claudius Gros and published by Springer Science & Business Media. This book was released on 2010-09-24 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover a wide range of findings in quantitative complex system science that help us make sense of our complex world. Written at an introductory level, the book provides an accessible entry into this fascinating and vitally important subject.
Download or read book Instabilities and Fronts in Extended Systems written by Pierre Collet and published by Princeton University Press. This book was released on 2014-07-14 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results often seem somewhat ad hoc, and it is not clear how to generalize them to the nextthat is, not yet solvedproblem. In an introduction to the subject of instabilities in spatially infinite systems, Pierre Collet and Jean-Pierre Eckmann aim to give a systematic account of these methods, and to work out the relevant features that make them operational. The book examines in detail a number of model equations from physics. The mathematical developments of the subject are based on bifurcation theory and on the theory of invariant manifolds. These are combined to give a coherent description of several problems in which instabilities occur, notably the Eckhaus instability and the formation of fronts in the Swift-Hohenberg equation. These phenomena can appear only in infinite systems, and this book breaks new ground as a systematic account of the mathematics connected with infinite space domains. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Dynamics of Complex Interacting Systems written by E. Goles and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the courses given at the Fourth School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 12th to 16th December 1994. This School brings together scientists working on subjects related to recent trends in complex systems. Some of these subjects deal with dynamical systems, ergodic theory, cellular automata, symbolic and arithmetic dynamics, spatial systems, large deviation theory and neural networks. Scientists working in these subjects come from several aeras: pure and applied mathematics, non linear physics, biology, computer science, electrical engineering and artificial intelligence. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Roberto Livi concerns the study of coupled map lattices (CML) as models of spatially extended dynamical systems. CML is one of the most used tools for the investigation of spatially extended systems. The paper emphasizes rigorous results about the dynamical behavior of one dimensional CML; i.e. a uniform real local function defined in the interval [0,1], interacting with its nearest neighbors in a one dimensional lattice.
Download or read book Complex Dynamics in Spatially Extended Systems written by and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Complexity of Dynamical Systems written by Johan Dubbeldam and published by John Wiley & Sons. This book was released on 2011-02-21 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.
Download or read book Noise in Spatially Extended Systems written by Jordi Garcia-Ojalvo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for graduates and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. It covers the theory of stochastic partial differential equations and gives an overview of the effects of external noise on dynamical systems with spatial degrees of freedom. Starting with a general introduction to noise-induced phenomena in dynamical systems, the text moves on to an extensive discussion of analytical and numerical tools needed to gain information from stochastic partial differential equations. It then turns to particular problems described by stochastic PDEs, covering a wide part of the rich phenomenology of spatially extended systems, such as nonequilibrium phase transitions, domain growth, pattern formation, and front propagation. The only prerequisite is a minimal background knowledge of the Langevin and Fokker-Planck equations.
Download or read book Complex Dynamics written by Lennart Carleson and published by Springer Science & Business Media. This book was released on 1996-02-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.
Download or read book Chaos and Socio Spatial Dynamics written by Dimitrios S. Dendrinos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a discrete in time-space universal map of relative dynamics that is used to unfold an extensive catalogue of dynamic events not previously discussed in mathematical or social science literature. With emphasis on the chaotic dynamics that may ensue, the book describes the evolution on the basis of temporal and locational advantages. It explains nonlinear discrete time dynamic maps primarily through numerical simulations. These very rich qualitative dynamics are linked to evolution processes in socio-spatial systems. Important features include: The analytical properties of the one-stock, two- and three-location map; the numerical results from the one- and two-stock, two- and three-location dynamics; and the demonstration of the map's potential applicability in the social sciences through simulating population dynamics of the U.S. Regions over a two-century period. In addition, this book includes new findings: the Hopf equivalent discrete time dynamics bifurcation; the Feigenbaum slope-sequences; the presence of strange local attractors and containers; switching of extreme states; the presence of different types of turbulence; local and global turbulence. Intended for researchers and advanced graduate students in applied mathematics and an interest in dynamics and chaos. Mathematical social scientists in many other fields will also find this book useful.
Download or read book Lyapunov Exponents written by Arkady Pikovsky and published by Cambridge University Press. This book was released on 2016-02-11 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.
Download or read book Copenhagen Conference on Complex Dynamics in Spatially Extended Systems Copenhagen 1995 written by Center for Chaos and Turbulence Studies and published by . This book was released on 1995 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Book of abstracts written by The Center for chaos and turbulence studies and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of Complex Dynamics written by Daniel S. Alexander and published by . This book was released on 2014-01-15 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Dynamics written by Vladimir G. Ivancevic and published by Springer. This book was released on 2007-09-17 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers learn to predict and control low- and high-dimensional as well as continuous- and discrete-time nonlinear systems dynamics in complex variables. In the final chapter, all the previously developed methods are used to present the "Holy Grail" of modern physical and cosmological science, the search for the "theory of everything" and the "true" cosmological dynamics.
Download or read book Numerical Continuation Methods for Dynamical Systems written by Bernd Krauskopf and published by Springer. This book was released on 2007-11-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Download or read book Final Report on Characterizing the Dynamics of Spatio temporal Data written by and published by . This book was released on 1998 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: One principal goal of the grant was to model and analyze the dynamics of spatially extended chaotic systems. One of the principal tools used in the analysis was KLTOOL, a computer package developed by the principal investigators for Karhunen-Loeve analysis. The package was used to analyze video data from a laboratory experiment on cellular flames. A second goal of the project was to analyze complex time series whose underlying dynamics may be low dimensionally chaotic. Particular emphasis was placed on systems of possible relevance to energy production and distribution. The work attempted to characterize low-dimensional aspects of the dynamics of a fluidized bed, in particular, a transition from periodic to irregular behavior. Finally, collaborators worked on aspects of targeting in chaotic dynamical systems. This work showed that it is possible to switch a moderately high-dimensional chaotic process rapidly between prespecified periodic saddle orbits embedding within the attractor. Additional work extended previously-developed algorithms for the highly accurate computation of stable manifolds of periodic saddle orbits, which is essential to the successful application of targeting algorithms.
Download or read book Dynamic Mode Decomposition written by J. Nathan Kutz and published by SIAM. This book was released on 2016-11-23 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.
