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Elegant Chaos

Elegant Chaos Author Julien C. Sprott
ISBN-10 9789812838827
Release 2010
Pages 304
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This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rossler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos.The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.

Advances and Applications in Chaotic Systems

Advances and Applications in Chaotic Systems Author Sundarapandian Vaidyanathan
ISBN-10 9783319302799
Release 2016-03-22
Pages 600
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This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

Chaos and Time series Analysis

Chaos and Time series Analysis Author Julien C. Sprott
ISBN-10 0198508395
Release 2003
Pages 507
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This text provides an introduction to the exciting new developments in chaos and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data, fractals, and complex systems. Most of the important elementary concepts in nonlinear dynamics arediscussed, with emphasis on the physical concepts and useful results rather than mathematical proofs and derivations. While many books on chaos are purely qualitative and many others are highly mathematical, this book fills the middle ground by giving the essential equations, but in the simplestpossible form. It assumes only an elementary knowledge of calculus. Complex numbers, differential equations, and vector calculus are used in places, but those tools are described as required. The book is aimed at the student, scientist, or engineer who wants to learn how to use the ideas in apractical setting. It is written at a level suitable for advanced undergraduate and beginning graduate students in all fields of science and engineering.

Strange Attractors

Strange Attractors Author Julien C. Sprott
ISBN-10 1558512985
Release 1993
Pages 426
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Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.

The Essence Of Chaos

The Essence Of Chaos Author Flavio Lorenzelli
ISBN-10 9780203214589
Release 2003-09-02
Pages 227
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The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.

Instabilities Chaos and Turbulence

Instabilities  Chaos and Turbulence Author Paul Manneville
ISBN-10 9781848163928
Release 2010
Pages 439
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This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Python Programming

Python Programming Author John M. Zelle
ISBN-10 9781887902991
Release 2004
Pages 517
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This book is suitable for use in a university-level first course in computing (CS1), as well as the increasingly popular course known as CS0. It is difficult for many students to master basic concepts in computer science and programming. A large portion of the confusion can be blamed on the complexity of the tools and materials that are traditionally used to teach CS1 and CS2. This textbook was written with a single overarching goal: to present the core concepts of computer science as simply as possible without being simplistic.

New Approaches and Concepts in Turbulence

New Approaches and Concepts in Turbulence Author T. Dracos
ISBN-10 3764329246
Release 1993-09-01
Pages 426
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This book contains the proceedings of a colloquium held in Monte Verità from September 9-13, 1991. Special care has been taken to devote adequate space to the scientific discussions, which claimed about half of the time available. Scientists from all over the world presented their views on the importance of kinematic properties, topology and fractal geometry, and on the dynamic behaviour of turbulent flows. They debated the importance of coherent structures and the possibility to incorporate these in the statistical theory of turbulence, as well as their significance for the reduction of the degrees of freedom and the prospective of dynamical systems and chaos approaches to the problem of turbulence. Also under discussion was the relevance of these new approaches to the study of the instability and the origin of turbulence, and the importance of numerical and physical experiments in improving the understanding of turbulence.

An Introduction to Mechanics

An Introduction to Mechanics Author Daniel Kleppner
ISBN-10 9780521198110
Release 2013-11-18
Pages 566
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This second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics.

Nonlinearity Chaos and Complexity

Nonlinearity  Chaos  and Complexity Author Cristoforo Sergio Bertuglia
ISBN-10 9780198567905
Release 2005
Pages 387
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Covering a broad range of topics and adopting a detailed philosophical approach to the subject, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences.

Nonlinear Dynamical Systems with Self Excited and Hidden Attractors

Nonlinear Dynamical Systems with Self Excited and Hidden Attractors Author Viet-Thanh Pham
ISBN-10 9783319712437
Release 2018-02-26
Pages 497
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This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems.

Exploring ODEs

Exploring ODEs Author Lloyd N. Trefethen
ISBN-10 9781611975161
Release 2017-12-21
Pages 335
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Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.

Advances in Chaos Theory and Intelligent Control

Advances in Chaos Theory and Intelligent Control Author Ahmad Taher Azar
ISBN-10 9783319303406
Release 2016-04-15
Pages 873
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The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate students, researchers, and practitioners in the areas of chaos theory and intelligent control.

Natural Biodynamics

Natural Biodynamics Author Vladimir G. Ivancevic
ISBN-10 9789812703163
Release 2005
Pages 1001
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This comprehensive volume is a graduate-level text in human biodynamics, written in the unified categorical language of modern differential geometry and topology. Combining mathematics, physics and robotics with human physiology, this is the first book that describes all levels of human biodynamics, from musculo-skeletal mechanics to the higher brain functions. The book develops and uses a variety of research methods, ranging from chaos theory and Haken's synergetics, through quantum mechanics, to nonlinear control and artificial intelligence, to provide the means to understand, predict and control the behavior of human-like systems in their full neuro-musculo-skeletal complexity. The applications of this unique scientific methodology range from prediction of human neuro-musculo-skeletal injuries to brain-like control of humanoid robots.

Indra s Pearls

Indra s Pearls Author David Mumford
ISBN-10 0521352533
Release 2002-04-25
Pages 395
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Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry.

Nonlinear Dynamics and Chaos

Nonlinear Dynamics and Chaos Author Steven H. Strogatz
ISBN-10 9780813349114
Release 2014-08-26
Pages 500
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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. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.

Chaos Theory Tamed

Chaos Theory Tamed Author Garnett Williams
ISBN-10 9781482295412
Release 2014-04-21
Pages 520
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This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents. Only basic algebra, trigonometry, geometry and statistics are assumed as background. The author focuses on the most important topics, very much with the general scientist in mind.