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ISBN 13 : 9814464791
Total Pages : pages
Book Rating : 4.8/5 (144 download)
Download or read book 2-D Quadratic Maps and 3-D ODE Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Elhadj Zeraoulia
Publisher : World Scientific
ISBN 13 : 9814307742
Total Pages : 357 pages
Book Rating : 4.8/5 (143 download)
Download or read book 2-D Quadratic Maps and 3-D ODE Systems written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2010 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the Hnon map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters. Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward Hnon mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincar map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincar mapping in addition to other analytical methods.
Author : Zeraoulia Elhadj
Publisher : CRC Press
ISBN 13 : 0429647425
Total Pages : 189 pages
Book Rating : 4.4/5 (296 download)
Download or read book Dynamical Systems written by Zeraoulia Elhadj and published by CRC Press. This book was released on 2019-01-21 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.
Author : Elhadj Zeraoulia
Publisher : World Scientific
ISBN 13 : 9814374075
Total Pages : 473 pages
Book Rating : 4.8/5 (143 download)
Download or read book Robust Chaos and Its Applications written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2012 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
Author : Zeraoulia Elhadj
Publisher : CRC Press
ISBN 13 : 1466580720
Total Pages : 338 pages
Book Rating : 4.4/5 (665 download)
Download or read book Lozi Mappings written by Zeraoulia Elhadj and published by CRC Press. This book was released on 2013-08-17 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable for such analysis. The book is not only a good introduction to the Lozi map and its generalizations, it also summarizes of important concepts in dynamical systems theory such as hyperbolicity, SRB measures, attractor types, and more.
Author : Goong Chen
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598299158
Total Pages : 243 pages
Book Rating : 4.5/5 (982 download)
Download or read book Chaotic Maps written by Goong Chen and published by Morgan & Claypool Publishers. This book was released on 2011-09-09 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. Table of Contents: Simple Interval Maps and Their Iterations / Total Variations of Iterates of Maps / Ordering among Periods: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant Sets / The Smale Horseshoe / Fractals / Rapid Fluctuations of Chaotic Maps on RN / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations
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ISBN 13 :
Total Pages : 1452 pages
Book Rating : 4.:/5 ( download)
Download or read book Publishers' circular and booksellers' record written by and published by . This book was released on 1881 with total page 1452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 1454 pages
Book Rating : 4.:/5 (334 download)
Download or read book The Publishers' Circular and General Record of British and Foreign Literature written by and published by . This book was released on 1881 with total page 1454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (91 download)
Download or read book Proceedings of the ... American Control Conference written by and published by . This book was released on 1983 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lawrence Perko
Publisher : Springer Science & Business Media
ISBN 13 : 1468402498
Total Pages : 530 pages
Book Rating : 4.4/5 (684 download)
Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.
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ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.:/5 (318 download)
Download or read book Proceedings of the 1983 American Control Conference written by and published by . This book was released on 1983 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 640 pages
Book Rating : 4.3/5 (91 download)
Download or read book American Journal of Physics written by and published by . This book was released on 1993 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 1452 pages
Book Rating : 4.3/5 (91 download)
Download or read book Publishers' Circular and Booksellers' Record of British and Foreign Literature written by and published by . This book was released on 1881 with total page 1452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 1878 pages
Book Rating : 4.0/5 ( download)
Download or read book Data Sources written by and published by . This book was released on 2000 with total page 1878 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gerald Teschl
Publisher : American Mathematical Society
ISBN 13 : 147047641X
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
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ISBN 13 :
Total Pages : 438 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geobyte written by and published by . This book was released on 1992 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.E/5 ( download)
Download or read book Educational Times written by and published by . This book was released on 1887 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:
