Chaos In Systems With Noise

Author : Tomasz Kapitaniak
Publisher : World Scientific
ISBN 13 : 9789810204105
Total Pages : 256 pages
Book Rating : 4.08/5 ( download)

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Download or read book Chaos in Systems with Noise written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1990 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.

Author : Andrzej Lasota
Publisher : Springer Science & Business Media
ISBN 13 : 146124286X
Total Pages : 481 pages
Book Rating : 4.64/5 ( download)

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Download or read book Chaos, Fractals, and Noise written by Andrzej Lasota and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.

Author : E. Roy Pike
Publisher : CRC Press
ISBN 13 : 1000156915
Total Pages : 282 pages
Book Rating : 4.11/5 ( download)

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Download or read book Chaos, Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Author : Francis C.M. Lau
Publisher : Springer Science & Business Media
ISBN 13 : 3662051834
Total Pages : 236 pages
Book Rating : 4.32/5 ( download)

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Download or read book Chaos-Based Digital Communication Systems written by Francis C.M. Lau and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first books in this area, this text focuses on important aspects of the system operation, analysis and performance evaluation of selected chaos-based digital communications systems – a hot topic in communications and signal processing.

Author : Stavros G. Stavrinides
Publisher : Springer Nature
ISBN 13 : 3030354415
Total Pages : 169 pages
Book Rating : 4.11/5 ( download)

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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.

Author : Yee Chun Lee
Publisher : World Scientific
ISBN 13 : 9789971505301
Total Pages : 430 pages
Book Rating : 4.04/5 ( download)

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Download or read book Evolution, Learning and Cognition written by Yee Chun Lee and published by World Scientific. This book was released on 1988 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review volume represents the first attempt to provide a comprehensive overview of this exciting and rapidly evolving development. The book comprises specially commissioned articles by leading researchers in the areas of neural networks and connectionist systems, classifier systems, adaptive network systems, genetic algorithm, cellular automata, artificial immune systems, evolutionary genetics, cognitive science, optical computing, combinatorial optimization, and cybernetics.

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 9814719714
Total Pages : 576 pages
Book Rating : 4.11/5 ( download)

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Download or read book Deterministic Chaos in One-Dimensional Continuous Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2016-03-14 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering. Contents:Bifurcational and Chaotic Dynamics of Simple Structural Members:BeamsPlatesPanelsShellsIntroduction to Fractal Dynamics:Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's SetIntroduction to Chaos and Wavelets:Routes to ChaosQuantifying Chaotic DynamicsSimple Chaotic Models:IntroductionAutonomous SystemsNon-Autonomous SystemsDiscrete and Continuous Dissipative Systems:IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D SystemsEuler-Bernoulli Beams:IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer BeamsTimoshenko and Sheremetev-Pelekh Beams:The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding RemarksPanels:Infinite Length PanelsCylindrical Panels of Infinite LengthPlates and Shells:Plates with Initial ImperfectionsFlexible Axially-Symmetric Shells Readership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers. Key Features:Includes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicistsCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scalesContains originally discovered, illustrated and discussed novel and/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators

Author : Tomasz Kapitaniak
Publisher :
ISBN 13 :
Total Pages : 85 pages
Book Rating : 4.76/5 ( download)

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Download or read book Chaos and Noise in Dynamical Systems written by Tomasz Kapitaniak and published by . This book was released on 1993 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Yurii Bolotin
Publisher : Springer
ISBN 13 : 3319424963
Total Pages : 281 pages
Book Rating : 4.65/5 ( download)

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Download or read book Chaos: Concepts, Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2016-10-24 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

Author : A.A. Tsonis
Publisher : Springer Science & Business Media
ISBN 13 : 1461533600
Total Pages : 279 pages
Book Rating : 4.03/5 ( download)

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Download or read book Chaos written by A.A. Tsonis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on chaos theory two very important points are clear: (I) random looking aperiodic behavior may be the product of determinism, and (2) nonlinear problems should be treated as nonlinear problems and not as simplified linear problems. The theoretical aspects ofchaos have been presented in great detail in several excellent books published in the last five years or so. However, while the problems associated with applications of the theory-such as dimension and Lyapunov exponentsestimation, chaosand nonlinear pre diction, and noise reduction-have been discussed in workshops and ar ticles, they have not been presented in book form. This book has been prepared to fill this gap between theory and ap plicationsand to assist studentsand scientists wishingto apply ideas from the theory ofnonlinear dynamical systems to problems from their areas of interest. The book is intended to be used as a text for an upper-level undergraduate or graduate-level course, as well as a reference source for researchers. My philosophy behind writing this book was to keep it simple and informative without compromising accuracy. I have made an effort to presentthe conceptsby usingsimplesystemsand step-by-stepderivations. Anyone with an understanding ofbasic differential equations and matrix theory should follow the text without difficulty. The book was designed to be self-contained. When applicable, examples accompany the theory. The reader will notice, however, that in the later chapters specific examples become less frequent. This is purposely done in the hope that individuals will draw on their own ideas and research projects for examples.