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Deterministic Chaos In One Dimensional Continuous Systems

2016-03-14 Science
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Release : 2016-03-14
Genre : Science
Kind : eBook
Book Rating : 714/5 ( reviews)

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Book Synopsis Deterministic Chaos In One Dimensional Continuous Systems by : Jan Awrejcewicz

Download or read book Deterministic Chaos In One Dimensional Continuous Systems written by Jan Awrejcewicz. This book was released on 2016-03-14. 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.

Chaotic Behaviour of Deterministic Dissipative Systems

1995-07-20 Science
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Release : 1995-07-20
Genre : Science
Kind : eBook
Book Rating : 308/5 ( reviews)

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Book Synopsis Chaotic Behaviour of Deterministic Dissipative Systems by : Milos Marek

Download or read book Chaotic Behaviour of Deterministic Dissipative Systems written by Milos Marek. This book was released on 1995-07-20. Available in PDF, EPUB and Kindle. Book excerpt: This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.

Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures

2019-05-28 Mathematics
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Release : 2019-05-28
Genre : Mathematics
Kind : eBook
Book Rating : 713/5 ( reviews)

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Book Synopsis Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures by : Gardini Laura

Download or read book Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures written by Gardini Laura. This book was released on 2019-05-28. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Deterministic Chaos

1995-04-15 Science
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Release : 1995-04-15
Genre : Science
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Deterministic Chaos by : Heinz Georg Schuster

Download or read book Deterministic Chaos written by Heinz Georg Schuster. This book was released on 1995-04-15. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised and updated 3rd edition of this highly regarded textbook. A new chapter on controlling chaos has been added. Translations into Japanese, Chinese, German, Russian and Polish demonstrate the international interest in this book. From reviews of former editions: In this book, Schuster gives a very useful summary of the main ideas of the subject as it now stands. Although a physist by training and style, he organizes his treatment by the logic of the mathematics, which is based on the concept of a dynamical system. Students about to begin research into chaos, and practising scientists new to the subject, will find this book well worth reading. Nature This text sets a standard which other authors and publishers in physics should strive to meet. Physics Bulletin

Chaos in One Dimensional Systems

2011-05
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Release : 2011-05
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Book Rating : 579/5 ( reviews)

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Book Synopsis Chaos in One Dimensional Systems by : Indranil Bhaumik

Download or read book Chaos in One Dimensional Systems written by Indranil Bhaumik. This book was released on 2011-05. Available in PDF, EPUB and Kindle. Book excerpt: Sir Isaac Newton conveyed to the real world the idea of modeling the motion of physical systems with equations. Nearly a hundred years ago it was known that deterministic systems can exhibit very complicated behavior. In the present day, scientists realize that the chaotic behavior can be observed almost in all domains of science and technology. Chaotic world reveals incomprehensibly complex behavior. In this book we have considered mainly some problems of discrete dynamical systems in one dimension. The problems have been selected very carefully. Most (but not all) of the results are pertaining to chaos. Some applications of chaos theory have also been discussed. The purpose of this book is to provide a textbook on discrete dynamical systems for the college or university students and also to help researchers pursuing this line of research. We strongly hope for wide acceptance of the contents of this book.

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