Analysis Of Chaotic Behavior In Non Linear Dynamical Systems

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Analysis of Chaotic Behavior in Non-linear Dynamical Systems

Author : Michał Piórek
Publisher : Springer
ISBN 13 : 3319948873
Total Pages : 132 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Analysis of Chaotic Behavior in Non-linear Dynamical Systems by : Michał Piórek

Download or read book Analysis of Chaotic Behavior in Non-linear Dynamical Systems written by Michał Piórek and published by Springer. This book was released on 2018-07-12 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All methods and algorithms are designed to allow detection of deterministic chaos behavior in quaternion data representing the rotation of a body in 3D space. This book is an excellent reference for engineers, researchers, and postgraduate students conducting research on human gait analysis, healthcare informatics, dynamical systems with deterministic chaos or time series analysis.

Frontiers in the Study of Chaotic Dynamical Systems with Open Problems

Author : Elhadj Zeraoulia
Publisher : World Scientific
ISBN 13 : 9814340707
Total Pages : 268 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Frontiers in the Study of Chaotic Dynamical Systems with Open Problems by : Elhadj Zeraoulia

Download or read book Frontiers in the Study of Chaotic Dynamical Systems with Open Problems written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2011 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.

Nonlinear Dynamics

Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
ISBN 13 : 3642556884
Total Pages : 628 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Nonlinear Dynamics by : Muthusamy Lakshmanan

Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Chaotic Dynamics

Author : Gregory L. Baker
Publisher : Cambridge University Press
ISBN 13 : 9780521471060
Total Pages : 282 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Chaotic Dynamics by : Gregory L. Baker

Download or read book Chaotic Dynamics written by Gregory L. Baker and published by Cambridge University Press. This book was released on 1996 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.

Analysis of Observed Chaotic Data

Author : Henry Abarbanel
Publisher : Springer Science & Business Media
ISBN 13 : 1461207630
Total Pages : 278 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Analysis of Observed Chaotic Data by : Henry Abarbanel

Download or read book Analysis of Observed Chaotic Data written by Henry Abarbanel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. It examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.

Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Author : Christos Volos
Publisher : MDPI
ISBN 13 : 3038978981
Total Pages : 290 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors by : Christos Volos

Download or read book Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors written by Christos Volos and published by MDPI. This book was released on 2019-05-03 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

Chaotic Motions in Nonlinear Dynamical Systems

Author : Wanda Szemplinska-Stupnicka
Publisher : Springer
ISBN 13 : 3709125960
Total Pages : 198 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Chaotic Motions in Nonlinear Dynamical Systems by : Wanda Szemplinska-Stupnicka

Download or read book Chaotic Motions in Nonlinear Dynamical Systems written by Wanda Szemplinska-Stupnicka and published by Springer. This book was released on 2014-05-04 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discoveries of chaotic, unpredictable behaviour in physical deterministic systems has brought about new analytic and experimental techniques in dynamics. The modern study of the new phenomena requires the analyst to become familiar with experiments (at least with numerical ones), since chaotic solutions cannot be written down, and it requires the experimenter to master the new concepts of the theory of nonlinear dynamical systems. This book is unique in that it presents both viewpoints: the viewpoint of the analyst and of the experimenter. In the first part F. Moon outlines the new experimental techniques which have emerged from the study of chaotic vibrations. These include Poincaré sections, fractial dimensions and Lapunov exponents. In the text by W. Szemplinska-Stupnicka the relation between the new chaotic phenomena and classical perturbation techniques is explored for the first time. In the third part G. Iooss presents methods of analysis for the calculations of bifurcations in nonlinear systems based on modern geometric mathematical concepts.

Chaotic Dynamics of Nonlinear Systems

Author : S. Neil Rasband
Publisher : Courier Dover Publications
ISBN 13 : 0486795993
Total Pages : 244 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Chaotic Dynamics of Nonlinear Systems by : S. Neil Rasband

Download or read book Chaotic Dynamics of Nonlinear Systems written by S. Neil Rasband and published by Courier Dover Publications. This book was released on 2015-08-19 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the concepts, applications, theory, and technique of chaos. Suitable for advanced undergraduates and graduate students and researchers. Requires familiarity with differential equations and linear vector spaces. 1990 edition.

Nonlinear Dynamical Systems and Chaos

Author : H.W. Broer
Publisher : Birkhäuser
ISBN 13 : 3034875185
Total Pages : 464 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Nonlinear Dynamical Systems and Chaos by : H.W. Broer

Download or read book Nonlinear Dynamical Systems and Chaos written by H.W. Broer and published by Birkhäuser. This book was released on 2013-11-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.

Nonlinear Time Series Analysis

Author : Holger Kantz
Publisher :
ISBN 13 : 9780521821506
Total Pages : 369 pages
Book Rating : 4.8/5 (215 download)

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Book Synopsis Nonlinear Time Series Analysis by : Holger Kantz

Download or read book Nonlinear Time Series Analysis written by Holger Kantz and published by . This book was released on 2004 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Chaos: Concepts, Control and Constructive Use

Author : Yurii Bolotin
Publisher : Springer
ISBN 13 : 3319424963
Total Pages : 281 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Chaos: Concepts, Control and Constructive Use by : Yurii Bolotin

Download or read book Chaos: Concepts, Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2016-10-24 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

Regularity and Complexity in Dynamical Systems

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 1461415233
Total Pages : 500 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Regularity and Complexity in Dynamical Systems by : Albert C. J. Luo

Download or read book Regularity and Complexity in Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-07-12 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Chaos

Author : Kathleen T. Alligood
Publisher : Springer Science & Business Media
ISBN 13 : 0387224920
Total Pages : 603 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Chaos by : Kathleen T. Alligood

Download or read book Chaos written by Kathleen T. Alligood and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.

An Introduction to Dynamical Systems and Chaos

Author : G. C. Layek
Publisher : Springer Nature
ISBN 13 : 9819976952
Total Pages : 701 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis An Introduction to Dynamical Systems and Chaos by : G. C. Layek

Download or read book An Introduction to Dynamical Systems and Chaos written by G. C. Layek and published by Springer Nature. This book was released on with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topology and Dynamics of Chaos

Author : Christophe Letellier
Publisher : World Scientific
ISBN 13 : 9814434876
Total Pages : 364 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology and Dynamics of Chaos by : Christophe Letellier

Download or read book Topology and Dynamics of Chaos written by Christophe Letellier and published by World Scientific. This book was released on 2013-01-11 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc. Contents:Introduction to Topological Analysis (Christophe Letellier & Robert Gilmore)Emergence of a Chaos Theory:The Peregrinations of Poincaré (R Abraham)A Toulouse Research Group in the “Prehistoric” Times of Chaotic Dynamics (Christian Mira)Can We Trust in Numerical Computations of Chaotic Solutions of Dynamical Systems? (René Lozi)Chaos Hierarchy — A Review, Thirty Years Later (Otto E Rössler & Christophe Letellier)Development of the Topology of Chaos:The Mathematics of Lorenz Knots (Joan S Birman)A Braided View of a Knotty Story (Mario Natiello & Hernán Solari)How Topology Came to Chaos (Robert Gilmore)Reflections From the Fourth Dimension (Marc Lefranc)The Symmetry of Chaos (Christophe Letellier)Applications of Chaos Theory:The Shape of Ocean Color (Nicholas Tufillaro)Low Dimensional Dynamics in Biological Motor Patterns (Gabriel B Mindlin)Minimal Smooth Chaotic Flows (Jean-Marc Malasoma)The Chaotic Marriage of Physics and Financial Economics (Claire Gilmore)Introduction of the Sphere Map with Application to Spin-Torque Nano-Oscillators (Keith Gilmore & Robert Gilmore)Robert Gilmore, a Portrait (Hernán G Solari) Readership: Graduate students and researchers interested in topological analysis of nonlinear dynamical systems producing chaotic attractors. Keywords:Chaos;Topology;Nonlinear DynamicsKey Features:Historical survey, main concepts and some applicationsIncludes contributions from most of the main scientists in the field (Rössler, Birman, and Lefranc)An introduction for beginners is included

Chaos in Systems with Noise

Author : Tomasz Kapitaniak
Publisher : World Scientific
ISBN 13 : 9789810204105
Total Pages : 256 pages
Book Rating : 4.2/5 (41 download)

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Book Synopsis Chaos in Systems with Noise by : Tomasz Kapitaniak

Download or read book Chaos in Systems with Noise written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1990 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.