Universal Scenarios Of Transitions To Chaos Via Homoclinic Bifurcations
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Universal Scenarios Of Transitions To Chaos Via Homoclinic Bifurcations
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Author : D. V. Lyubimov
language : en
Publisher: CRC Press
Release Date : 1989
Universal Scenarios Of Transitions To Chaos Via Homoclinic Bifurcations written by D. V. Lyubimov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Science categories.
Difference Equations Discrete Dynamical Systems And Applications
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Author : Saber Elaydi
language : en
Publisher: Springer
Release Date : 2019-06-29
Difference Equations Discrete Dynamical Systems And Applications written by Saber Elaydi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-29 with Mathematics categories.
The book presents the proceedings of the 23rd International Conference on Difference Equations and Applications, ICDEA 2017, held at the West University of Timișoara, Romania, under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28, 2017. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences. Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in the field.
Chaos In Electronics
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Author : M.A. van Wyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Chaos In Electronics written by M.A. van Wyk 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 2013-06-29 with Technology & Engineering categories.
Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures
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Author : Viktor Avrutin
language : en
Publisher: World Scientific
Release Date : 2019-05-28
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures written by Viktor Avrutin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-28 with Mathematics categories.
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.
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems
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Author : Bernold Fiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems written by Bernold Fiedler 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.
This book summarizes and highlights progress in our understanding of Dy namical Systems during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems" . The program was funded by the Deutsche Forschungsgemeinschaft (DFG) and aimed at combining, focussing, and enhancing research efforts of active groups in the field by cooperation on a federal level. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications far into the neighboring disciplines of Science. Three fundamental topics in Dynamical Systems are at the core of our research effort: behavior for large time dimension measure, and chaos Each of these topics is, of course, a highly complex problem area in itself and does not fit naturally into the deplorably traditional confines of any of the disciplines of ergodic theory, analysis, or numerical analysis alone. The necessity of mathematical cooperation between these three disciplines is quite obvious when facing the formidahle task of establishing a bidirectional transfer which bridges the gap between deep, detailed theoretical insight and relevant, specific applications. Both analysis and numerical analysis playa key role when it comes to huilding that bridge. Some steps of our joint bridging efforts are collected in this volume. Neither our approach nor the presentations in this volume are monolithic.
Nonlinear Science And Complexity Proceedings Of The Conference
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Author : Albert C J Luo
language : en
Publisher: World Scientific
Release Date : 2006-12-09
Nonlinear Science And Complexity Proceedings Of The Conference written by Albert C J Luo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-09 with Science categories.
This volume provides useful tools in Lie group analysis to solve nonlinear partial differential equations. Many of important issues in nonlinear wave dynamics and nonlinear fluid mechanics are presented: Homotopy techniques are used to obtain analytical solutions; fundamental problems and theories in classic and quantum dynamical systems are discussed; and numerous interesting results about dynamics and vibration in sensor and smart systems are presented. Interval computation and nonlinear modeling in dynamics and control are also briefly included.
Multidimensional Strange Attractors And Turbulence
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Author : I. S. Aranson
language : en
Publisher: CRC Press
Release Date : 1989
Multidimensional Strange Attractors And Turbulence written by I. S. Aranson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
The authors explore the origin of multidimensional strange attractors and their role in describing turbulence. It includes an analytical estimation of the deminsions of strange attractors for models described by differential-difference equations and discusses the conditions in which space-homogeneous chaos is stable with respect to random perturbations in flow systems.
Nonlinearity Bifurcation And Chaos
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Author : Jan Awrejcewicz
language : en
Publisher: BoD – Books on Demand
Release Date : 2012-10-24
Nonlinearity Bifurcation And Chaos written by Jan Awrejcewicz and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-24 with Mathematics categories.
Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.
Geometric Integration Theory On Supermanifolds
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Author : T. Voronov
language : en
Publisher: CRC Press
Release Date : 1991
Geometric Integration Theory On Supermanifolds written by T. Voronov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The author presents the first detailed and original account of his theory of forms on supermanifolds-a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The paper develops the apparatus of supermanifold differential topology necessary for the integration theory. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism, which sets out afresh such challenging problems as the Berezin intgegral on a bounded domain.
Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems
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Author : I. M. Krichever
language : en
Publisher: CRC Press
Release Date : 1992
Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems written by I. M. Krichever and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.