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Author: Tomasz Kapitaniak
Publisher: World Scientific
ISBN: 9814502774
Category : Science
Languages : en
Pages : 100
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Book Description
This book discusses the influence of quasiperiodic force on dynamical system. With this type of forcing, different types of attractors are possible, for example, strange nonchaotic attractors which have some unusual properties. The main part of this book is based on the authors' recent works, but it also presents the results which are the combined achievements of many investigators. Contents:IntroductionAttractors of Dynamical SystemsStrange Nonchaotic AttractorsInhibition of Chaotic Behaviour in Coupled Geophysical ModelsExperimental System with Dry Friction Readership: Scientists interested in chaos and nonlinear science. keywords: “… useful as a first reading in this particular subfield of nonlinear dynamics.” Mathematical Reviews
Author: Tomasz Kapitaniak
Publisher: World Scientific
ISBN: 9814502774
Category : Science
Languages : en
Pages : 100
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Book Description
This book discusses the influence of quasiperiodic force on dynamical system. With this type of forcing, different types of attractors are possible, for example, strange nonchaotic attractors which have some unusual properties. The main part of this book is based on the authors' recent works, but it also presents the results which are the combined achievements of many investigators. Contents:IntroductionAttractors of Dynamical SystemsStrange Nonchaotic AttractorsInhibition of Chaotic Behaviour in Coupled Geophysical ModelsExperimental System with Dry Friction Readership: Scientists interested in chaos and nonlinear science. keywords: “… useful as a first reading in this particular subfield of nonlinear dynamics.” Mathematical Reviews
Author: Arkady S Pikovsky
Publisher: World Scientific
ISBN: 9814478768
Category : Science
Languages : en
Pages : 226
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Book Description
This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed.
Author: Ulrike Feudel
Publisher: World Scientific
ISBN: 9812774408
Category : Science
Languages : en
Pages : 226
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Book Description
This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed. Sample Chapter(s). Chapter 1: Introduction (122 KB). Contents: Models; Rational Approximations; Stability and Instability; Fractal and Statistical Properties; Bifurcations in Quasiperiodically Forced Systems and Transitions to SNA; Renormalization Group Approach to the Onset of SNA in Maps with the Golden-Mean Quasiperiodic Driving. Readership: Graduate students and researchers in nonlinear science.
Author: Tobias H. Jger
Publisher: American Mathematical Soc.
ISBN: 082184427X
Category : Mathematics
Languages : en
Pages : 120
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Book Description
The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.
Author: Vladimir G. Ivancevic
Publisher: Springer Science & Business Media
ISBN: 1402054564
Category : Science
Languages : en
Pages : 711
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Book Description
This graduate–level textbook is devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincaré’s 3-body problem, high-tech Josephson junctions, and more.
Author: Kapitaniak Tomasz
Publisher: World Scientific
ISBN: 9814550213
Category :
Languages : en
Pages : 320
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Book Description
This volume contains a selection of papers presented at Euromech Colloquium 308 — Chaos and Noise in Dynamical Systems.Roughly speaking, a chaotic solution to an ordinary differential equation is aperiodic and “looks like” a stochastic process. On the other hand, the theory of probability and stochastic processes was developed to describe complicated irregular phenomena taking place in the real world, which in most cases are chaotic. This observation led to the idea of bringing together experts on both nonlinear chaotic and stochastic systems for the conference. Equal attention was given to recent theoretical results and practical applications.The revised and updated papers in this volume are grouped in the following sections: Theory of Chaotic Systems; Stochastic Systems; Spatiotemporal Systems and Fluid Dynamics; Numerical Tools; and Practical Applications. Each section starts with a short introduction and a brief summary of the presented papers.
Author: Edward Ott
Publisher: Cambridge University Press
ISBN: 1139936573
Category : Science
Languages : en
Pages : 500
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Book Description
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.
Author:
Publisher:
ISBN:
Category : Power resources
Languages : en
Pages : 656
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Book Description
Author: Attilio Maccari
Publisher: John Wiley & Sons
ISBN: 3527414215
Category : Science
Languages : en
Pages : 261
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Book Description
Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension. To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics. Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as: Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs) Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.
Author: T Kapitaniak
Publisher: World Scientific
ISBN: 9814506214
Category : Medical
Languages : en
Pages : 668
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Book Description
This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection. Contents: Chaos before Chaos:Frequency Demultiplication (B Van der Pol & J Van der Mark)Description and Quantification of Chaotic Behavior:Geometry from a Time Series (N H Packard et al.)Analytical Methods:A Partial Differential Equation with Infinitely Many Periodic Orbits: Chaotic Oscillations of a Forced Beam (P Holmes & J Marsden)Classical Nonlinear Oscillators: Duffing, Van der Pol and Pendulum:Universal Scaling Property in Bifurcation Structure of Duffing's and Generalized Duffing's Equations (S Sato et al.)Other Oscillatory Systems:Complex Dynamics of Compliant Off-Shore Structures (J M T Thompson)Chaos in Noisy Systems:Fluctuations and the Onset of Chaos (J P Crutchfield & B A Huberman)Strange Nonchaotic Attractors:Dimensions of Strange Nonchaotic Attractors (M Ding et al.)Spatial Chaos:Chaos as a Limit in a Boundary Value Problem (C Kahlert & O E Rössler)Fractal Basin Boundaries:Fractal Basin Boundaries and Homoclinic Orbit for Periodic Motion in a Two-Well Potential (F C Moon & G-H Li)and other papers Readership: Nonlinear scientists, applied mathematicians, engineers and physicists. keywords:
