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Author: Polina S. Landa
Publisher: Springer Science & Business Media
ISBN: 3540452524
Category : Mathematics
Languages : en
Pages : 401
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Book Description
This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Author: Polina S. Landa
Publisher: Springer Science & Business Media
ISBN: 3540452524
Category : Mathematics
Languages : en
Pages : 401
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Book Description
This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Author: Tomasz Kapitaniak
Publisher: Manchester University Press
ISBN: 9780719033643
Category : Health & Fitness
Languages : en
Pages : 240
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Book Description
Author: A.J. Lichtenberg
Publisher: Springer Science & Business Media
ISBN: 1475721846
Category : Mathematics
Languages : en
Pages : 708
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Book Description
This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.
Author: Juri I. Neimark
Publisher: Springer Science & Business Media
ISBN: 9401125961
Category : Mathematics
Languages : en
Pages : 510
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Book Description
This volume is devoted to stochastic and chaotic oscillations in dissipative systems. Chapter 1 deals with mathematical models of deterministic, discrete and distributed dynamical systems. In Chapter 2, the two basic trends of order and chaos are considered. The next three chapters describe stochasticity transformers, amplifiers and generators, turbulence, and phase portraits of steady-state motions and their bifurcations. Chapter 6 treats the topics of stochastic and chaotic attractors, and this is followed by two chapters dealing with routes to chaos and the quantitative characteristics of stochastic and chaotic motions. Finally, Chapter 9, which comprises more than one-third of the book, presents examples of systems having chaotic and stochastic motions drawn from mechanical, physical, chemical and biological systems. The book concludes with a comprehensive bibliography. For mathematicians, physicists, chemists and biologists interested in stochastic and chaotic oscillations in dynamical systems.
Author: Aleksandr L?vovich Fradkov
Publisher: World Scientific
ISBN: 9789810230692
Category : Science
Languages : en
Pages : 410
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Book Description
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
Author: V. V. Matrosov
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
Author: V. B. Bhatia
Publisher: Alpha Science Int'l Ltd.
ISBN: 9788173191053
Category : Reference
Languages : en
Pages : 372
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Book Description
The book covers the traditional classical mechanics and then introduces nonlinear oscillations and chaos. These subjects, particularly chaos, have become very important in the recent years and are now being included in courses in Physics and elsewhere. Even within classical mechanics subjects such as nearly circular orbits, virial theorem, anharmonic oscillator and precession and nutation of the earth have been included to make the book suit varied requirements. The book can be adopted for foundation courses on classical mechanics at graduate and post-graduate levels in physics, mathematics and astronomy and wherever else classical mechanics may be a requirement.A large number of problems interspersed throughout the text will induce the students to test the knowledge they had acquired before proceeding further. Another important feature is the appendix which contains some computer programs with essential instructions for solving integrals and differential equations and for plotting phase trajectories and strange attractors on the computer screen so that a student could draw these graphs independently.The short biographical sketches of great scientists and mathematicians who made important contributions to the subject might inspire some readers to look up the detailed biographies to gain some insight the way the science develops.
Author: Otto E. Rössler
Publisher: Springer Nature
ISBN: 3030443051
Category : Science
Languages : en
Pages : 242
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Book Description
Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never been published elsewhere. The manuscript has now been edited by Christophe Letellier - involved in chaos theory for almost three decades himself, as well as being active in the history of sciences - with a minimum of changes to the original text. Finally released for the benefit of specialists and non-specialists alike, this book is equally interesting from the historical and the scientific points of view: an unconventionally modern approach to chaos theory, it can be read as a classic introduction and short monograph as well as a collection of original insights into advanced topics from this field.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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Book Description
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.
Author: Frank C. Hoppensteadt
Publisher: Springer Science & Business Media
ISBN: 1475722753
Category : Mathematics
Languages : en
Pages : 321
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Book Description
Analysis and Simulation of Chaotic Systems is a text designed to be used at the graduate level in applied mathematics for students from mathematics, engineering, physics, chemistry and biology. The book can be used as a stand-alone text for a full year course or it can be heavily supplemented with material of more mathematical, more engineering or more scientific nature. Computations and computer simulations are used throughout this text to illustrate phenomena discussed and to supply readers with probes to use on new problems.
