Dynamical Chaos Models And Experiments Appearance Routes And Stru Of Chaos In Simple Dyna Systems
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Dynamical Chaos Models And Experiments Appearance Routes And Stru Of Chaos In Simple Dyna Systems
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Author : Vadim S Anishchenko
language : en
Publisher: World Scientific
Release Date : 1995-09-19
Dynamical Chaos Models And Experiments Appearance Routes And Stru Of Chaos In Simple Dyna Systems written by Vadim S Anishchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-19 with Science categories.
In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.
Dynamical Chaos
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Author : Vadim Semenovich Anishchenko
language : en
Publisher: World Scientific
Release Date : 1995
Dynamical Chaos written by Vadim Semenovich Anishchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
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.
Elegant Chaos Algebraically Simple Chaotic Flows
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Author : Julien Clinton Sprott
language : en
Publisher: World Scientific
Release Date : 2010-03-22
Elegant Chaos Algebraically Simple Chaotic Flows written by Julien Clinton Sprott and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-22 with Mathematics categories.
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, Rössler, 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.
Chaos
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Author : Kathleen Alligood
language : en
Publisher: Springer
Release Date : 2012-12-06
Chaos written by Kathleen Alligood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
Bulletin
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Author : Institute of Mathematics and Its Applications
language : en
Publisher:
Release Date : 1994
Bulletin written by Institute of Mathematics and Its Applications and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Chaos And Nonlinear Dynamics
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Author : Robert C. Hilborn
language : en
Publisher: Oxford University Press, USA
Release Date : 1994
Chaos And Nonlinear Dynamics written by Robert C. Hilborn and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Mathematics of Computing -- Miscellaneous.
Complexity Chaos And Biological Evolution
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Author : Erik Mosekilde
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Complexity Chaos And Biological Evolution written by Erik Mosekilde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Science categories.
From time to time, perhaps a few times each century, a revolution occurs that questions some of our basic beliefs and sweeps across otherwise well guarded disciplinary boundaries. These are the periods when science is fun, when new paradigms have to be formulated, and when young scientists can do serious work without first having to acquire all the knowledge of their teachers. The emergence of nonlinear science appears to be one such revolution. In a surprising manner, this new science has disclosed a number of misconceptions in our traditional understanding of determinism. In particular, it has been shown that the notion of predictability, according to which the trajectory of a system can be precisely determined if one knows the equations of motion and the initial conditions, is related to textbook examples of simple; integrable systems. This predictability does not extend to nonlinear, conservative systems in general. Dissipative systems can also show unpredictability, provided that the motion is sustained by externally supplied energy and/or resources. These discoveries, and the associated discovery that even relatively simple nonlinear systems can show extremely complex behavior, have brought about an unprecedented feeling of common interest among scientists from many different disciplines. During the last decade or two we have come to understand that there are universal routes to chaos, we have learned about stretching and folding, and we have discovered the beautiful fractal geometry underlying chaotic attractors.
Understanding Nonlinear Dynamics
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Author : Daniel Kaplan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Understanding Nonlinear Dynamics written by Daniel Kaplan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.
The Software Encyclopedia
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Author :
language : en
Publisher:
Release Date : 1986
The Software Encyclopedia written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Computer industry categories.