2 D Quadratic Maps And 3 D Ode Systems PDF Download
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Author | : Elhadj Zeraoulia |
Publisher | : World Scientific |
Total Pages | : 357 |
Release | : 2010 |
Genre | : Science |
ISBN | : 9814307742 |
Download 2-D Quadratic Maps and 3-D ODE Systems Book in PDF, ePub and Kindle
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 |
Total Pages | : 189 |
Release | : 2019-01-21 |
Genre | : Mathematics |
ISBN | : 0429647425 |
Download Dynamical Systems Book in PDF, ePub and Kindle
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 | : Zeraoulia Elhadj |
Publisher | : CRC Press |
Total Pages | : 334 |
Release | : 2013-08-17 |
Genre | : Mathematics |
ISBN | : 1466580720 |
Download Lozi Mappings Book in PDF, ePub and Kindle
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 fo
Author | : |
Publisher | : |
Total Pages | : 738 |
Release | : 1881 |
Genre | : |
ISBN | : |
Download Publishers' circular and booksellers' record Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 1452 |
Release | : 1881 |
Genre | : Bibliography |
ISBN | : |
Download Publishers' Circular and Booksellers' Record of British and Foreign Literature Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 1454 |
Release | : 1881 |
Genre | : Bibliography |
ISBN | : |
Download The Publishers' Circular and General Record of British and Foreign Literature Book in PDF, ePub and Kindle
Author | : Lawrence Perko |
Publisher | : Springer Science & Business Media |
Total Pages | : 530 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468402498 |
Download Differential Equations and Dynamical Systems Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 404 |
Release | : 1983 |
Genre | : Automatic control |
ISBN | : |
Download Proceedings of the ... American Control Conference Book in PDF, ePub and Kindle
Author | : Gerald Teschl |
Publisher | : American Mathematical Soc. |
Total Pages | : 356 |
Release | : 2012-08-30 |
Genre | : Mathematics |
ISBN | : 0821883283 |
Download Ordinary Differential Equations and Dynamical Systems Book in PDF, ePub and Kindle
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 Poincare-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.
Author | : |
Publisher | : |
Total Pages | : 402 |
Release | : 1983 |
Genre | : Automatic control |
ISBN | : |
Download Proceedings of the 1983 American Control Conference, Sheraton-Palace Hotel, San Francisco, California, June 22, 23, 24, 1983 Book in PDF, ePub and Kindle