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Bifurcation and Chaos in Complex Systems

Author:

Publisher: Elsevier

Published: 2006-06-30

Total Pages: 400

ISBN-13: 9780080462660

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The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems. · New Views for Difficult Problems · Novel Ideas and Concepts · Hilbert's 16th Problem · Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems · Stochastic and Fuzzy Nonlinear Dynamical Systems · Fuzzy Bifurcation · Parametrical, Nonlinear Systems · Mode Interactions in nonlinear dynamical systems

Book Synopsis Bifurcation and Chaos in Complex Systems by :

Download or read book Bifurcation and Chaos in Complex Systems written by and published by Elsevier. This book was released on 2006-06-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems. · New Views for Difficult Problems · Novel Ideas and Concepts · Hilbert's 16th Problem · Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems · Stochastic and Fuzzy Nonlinear Dynamical Systems · Fuzzy Bifurcation · Parametrical, Nonlinear Systems · Mode Interactions in nonlinear dynamical systems

Complex Systems: Chaos and Beyond

Author: Kunihiko Kaneko

Publisher: Springer Science & Business Media

Published: 2011-06-28

Total Pages: 284

ISBN-13: 3642568610

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This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.

Book Synopsis Complex Systems: Chaos and Beyond by : Kunihiko Kaneko

Download or read book Complex Systems: Chaos and Beyond written by Kunihiko Kaneko and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.

Chaos in Dynamical Systems

Author: Edward Ott

Publisher: Cambridge University Press

Published: 2002-08-22

Total Pages: 500

ISBN-13: 9780521010849

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Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.

Book Synopsis Chaos in Dynamical Systems by : Edward Ott

Download or read book Chaos in Dynamical Systems written by Edward Ott and published by Cambridge University Press. This book was released on 2002-08-22 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.

Chaos and Complex Systems

Author: Stavros G. Stavrinides

Publisher: Springer Nature

Published: 2020-02-19

Total Pages: 169

ISBN-13: 3030354415

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This book presents the proceedings of the “5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS).” All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.

Book Synopsis Chaos and Complex Systems by : Stavros G. Stavrinides

Download or read book Chaos and Complex Systems written by Stavros G. Stavrinides and published by Springer Nature. This book was released on 2020-02-19 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the “5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS).” All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.

Discrete Dynamical Systems, Bifurcations and Chaos in Economics

Author: Wei-Bin Zhang

Publisher: Elsevier

Published: 2006-01-05

Total Pages: 459

ISBN-13: 0080462464

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This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics. A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics Mathematical definitions and theorems are introduced in a systematic and easily accessible way Examples are from almost all fields of economics; technically proceeding from basic to advanced topics Lively illustrations with numerous figures Numerous simulation to see paths of economic dynamics Comprehensive treatment of the subject with a comprehensive and easily accessible approach

Book Synopsis Discrete Dynamical Systems, Bifurcations and Chaos in Economics by : Wei-Bin Zhang

Download or read book Discrete Dynamical Systems, Bifurcations and Chaos in Economics written by Wei-Bin Zhang and published by Elsevier. This book was released on 2006-01-05 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics. A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics Mathematical definitions and theorems are introduced in a systematic and easily accessible way Examples are from almost all fields of economics; technically proceeding from basic to advanced topics Lively illustrations with numerous figures Numerous simulation to see paths of economic dynamics Comprehensive treatment of the subject with a comprehensive and easily accessible approach

Chaos and Dynamical Systems

Author: David P. Feldman

Publisher: Princeton University Press

Published: 2019-08-06

Total Pages: 262

ISBN-13: 0691161526

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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.

Book Synopsis Chaos and Dynamical Systems by : David P. Feldman

Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chaos and Complex Systems

Author: Stavros G. Stavrinides

Publisher: Springer Science & Business Media

Published: 2013-03-19

Total Pages: 559

ISBN-13: 364233914X

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Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysics, and from nonlinear analysis to the history of chaos theory. The corresponding proceedings collected in this volume address a broad spectrum of contemporary topics, including but not limited to networks, circuits, systems, biology, evolution and ecology, nonlinear dynamics and pattern formation, as well as neural, psychological, psycho-social, socio-economic, management complexity and global systems.

Book Synopsis Chaos and Complex Systems by : Stavros G. Stavrinides

Download or read book Chaos and Complex Systems written by Stavros G. Stavrinides and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysics, and from nonlinear analysis to the history of chaos theory. The corresponding proceedings collected in this volume address a broad spectrum of contemporary topics, including but not limited to networks, circuits, systems, biology, evolution and ecology, nonlinear dynamics and pattern formation, as well as neural, psychological, psycho-social, socio-economic, management complexity and global systems.

Bifurcation and Chaos in Fractional-Order Systems

Author: Marius-F. Danca

Publisher: MDPI

Published: 2021-01-19

Total Pages: 108

ISBN-13: 3036500928

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This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics.

Book Synopsis Bifurcation and Chaos in Fractional-Order Systems by : Marius-F. Danca

Download or read book Bifurcation and Chaos in Fractional-Order Systems written by Marius-F. Danca and published by MDPI. This book was released on 2021-01-19 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics.

Bifurcations and Chaos in Piecewise-smooth Dynamical Systems

Author: Zhanybai T. Zhusubaliyev

Publisher: World Scientific

Published: 2003

Total Pages: 377

ISBN-13: 9812384200

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Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Book Synopsis Bifurcations and Chaos in Piecewise-smooth Dynamical Systems by : Zhanybai T. Zhusubaliyev

Download or read book Bifurcations and Chaos in Piecewise-smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and published by World Scientific. This book was released on 2003 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Bifurcation and Chaos in Fractional-Order Systems

Author: Marius-F. Danca

Publisher:

Published: 2021

Total Pages: 108

ISBN-13: 9783036500935

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Book Synopsis Bifurcation and Chaos in Fractional-Order Systems by : Marius-F. Danca

Download or read book Bifurcation and Chaos in Fractional-Order Systems written by Marius-F. Danca and published by . This book was released on 2021 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics.