Chaotic Dynamics In Two Dimensional Noninvertible Maps

Author : C. Mira
Publisher : World Scientific
Page : 638 pages
File Size : 49,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9810216475

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Chaotic Dynamics in Two-dimensional Noninvertible Maps by C. Mira Pdf

This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.

Author : Ralph Abraham,Laura Gardini,Christian Mira
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 55,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461219361

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Chaos in Discrete Dynamical Systems by Ralph Abraham,Laura Gardini,Christian Mira Pdf

The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9789814478984

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Modeling and Computations in Dynamical Systems by Anonim Pdf

Author : Wilfrid Perruquetti,Jean-Pierre Barbot
Publisher : CRC Press
Page : 318 pages
File Size : 40,6 Mb
Release : 2018-10-03
Category : Technology & Engineering
ISBN : 9781351836814

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Chaos in Automatic Control by Wilfrid Perruquetti,Jean-Pierre Barbot Pdf

Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field. Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography. Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.

Author : Tamás Tél,Márton Gruiz
Publisher : Cambridge University Press
Page : 440 pages
File Size : 55,9 Mb
Release : 2006-08-24
Category : Mathematics
ISBN : 0521547830

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Chaotic Dynamics by Tamás Tél,Márton Gruiz Pdf

A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556883

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author : Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić
Publisher : Springer Nature
Page : 534 pages
File Size : 40,7 Mb
Release : 2023-03-25
Category : Mathematics
ISBN : 9783031252259

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Advances in Discrete Dynamical Systems, Difference Equations and Applications by Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić Pdf

​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Author : Kapitaniak Tomasz,Brindley John
Publisher : World Scientific
Page : 320 pages
File Size : 45,6 Mb
Release : 1994-10-28
Category : Electronic
ISBN : 9789814550215

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Chaos And Nonlinear Mechanics: Proceedings Of Euromech Colloquium 308 "Chaos And Noise In Dynamical Systems" by Kapitaniak Tomasz,Brindley John Pdf

This volume contains a selection of papers presented at Euromech Colloquium 308 — Chaos and Noise in Dynamical Systems.Roughly speaking, a chaotic solution to an ordinary differential equation is aperiodic and “looks like” a stochastic process. On the other hand, the theory of probability and stochastic processes was developed to describe complicated irregular phenomena taking place in the real world, which in most cases are chaotic. This observation led to the idea of bringing together experts on both nonlinear chaotic and stochastic systems for the conference. Equal attention was given to recent theoretical results and practical applications.The revised and updated papers in this volume are grouped in the following sections: Theory of Chaotic Systems; Stochastic Systems; Spatiotemporal Systems and Fluid Dynamics; Numerical Tools; and Practical Applications. Each section starts with a short introduction and a brief summary of the presented papers.

Author : Iryna Sushko
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 51,5 Mb
Release : 2006-08-13
Category : Business & Economics
ISBN : 9783540321682

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Business Cycle Dynamics by Iryna Sushko Pdf

Business cycle theory has been one of the fastest growing fields in modern nonlinear economic dynamics. This book presents new mathematical methods for global analysis which have not previously been available in this easily accessible form. In addition it contains a presentation of full analyses of several models left open in the 1950s when the tools then available did not permit more systematic analysis.

Author : Irina Sushko
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 50,7 Mb
Release : 2013-03-19
Category : Business & Economics
ISBN : 9783540247920

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Oligopoly Dynamics by Irina Sushko Pdf

These proceedings are from a conference held at the Centre for Regional Science (CERUM) at Umea Umeâ University, Sweden, 17-18 June 2001. Unlike Un1ike many conference proceedings, this volume contains only on1y invited invited contribu contribu tions tions on specified topics so as to make the book coherent and self-contained. The authors and editors hope that this coherence will make the volume use fu1 fuI also as a text for courses in industrial organisation. To this end two chap ters on the history of oligopoly theory, from the beginnings with Cournot 1838, to the present day, and one chapter on modem methods for analysing iterated discrete time maps, have been inserted at the beginning ofthe book. Unlike Un1ike most current literature on games and oligopoly, this book is not focused on the usual topics of game theory: optimal strategies, dominance, and equilibrium. Rather it is the evolutionary dynamics, often of a complex type, inc1uding deterministic chaos, which are in focus. The contributions, after the historical and the methodological introductions, represent various segments of the research frontier in this area, though pains have been taken to tie some of the models to a number of most promising contributions from the frugal period 1929-1941, which have suffered from unjust neglect in the following industrial organisation literature.

Author : Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio
Publisher : World Scientific
Page : 648 pages
File Size : 49,6 Mb
Release : 2019-05-28
Category : Mathematics
ISBN : 9789811204715

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Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures by Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio Pdf

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.

Author : Jerzy A. Filar,Vladimir Gaitsgory,Koichi Mizukami
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213369

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Advances in Dynamic Games and Applications by Jerzy A. Filar,Vladimir Gaitsgory,Koichi Mizukami Pdf

Modem game theory has evolved enonnously since its inception in the 1920s in the works ofBorel and von Neumann and since publication in the 1940s of the seminal treatise "Theory of Games and Economic Behavior" by von Neumann and Morgenstern. The branch of game theory known as dynamic games is-to a significant extent-descended from the pioneering work on differential games done by Isaacs in the 1950s and 1960s. Since those early decades game theory has branched out in many directions, spanning such diverse disciplines as mathematics, economics, electrical and electronics engineering, operations research, computer science, theoretical ecology, environmental science, and even political science. The papers in this volume reflect both the maturity and the vitality of modem day game theory in general, and of dynamic games, in particular. The maturity can be seen from the sophistication of the theorems, proofs, methods, and numerical algorithms contained in these articles. The vitality is manifested by the range of new ideas, new applications, the numberofyoung researchers among the authors, and the expanding worldwide coverage of research centers and institutes where the contributions originated

Author : Saber Elaydi,Christian Pötzsche,Adina Luminiţa Sasu
Publisher : Springer
Page : 382 pages
File Size : 54,6 Mb
Release : 2019-06-29
Category : Mathematics
ISBN : 9783030200169

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Difference Equations, Discrete Dynamical Systems and Applications by Saber Elaydi,Christian Pötzsche,Adina Luminiţa Sasu Pdf

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.

Author : Gian Italo Bischi,Carl Chiarella,Michael Kopel,Ferenc Szidarovszky
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 47,7 Mb
Release : 2009-12-01
Category : Business & Economics
ISBN : 9783642021060

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Nonlinear Oligopolies by Gian Italo Bischi,Carl Chiarella,Michael Kopel,Ferenc Szidarovszky Pdf

This book presents the latest trends, methods and results in nonlinear dynamics with a special focus on oligopolies. It contains a number of technical appendices that summarize techniques of global dynamics not easily accessible elsewhere.

Author : Christian Mira
Publisher : World Scientific
Page : 472 pages
File Size : 51,5 Mb
Release : 1987-10-01
Category : Electronic
ISBN : 9789814603447

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Chaotic Dynamics: From The One-dimensional Endomorphism To The Two-dimensional Diffeomorphism by Christian Mira Pdf

Contents: Dynamical Systems and Recurrences. GeneralitiesSome Properties of One-Dimensional Recurrences (Maps)Myrberg's Results on the One-Dimensional Quadratic Recurrences. Their ConsequencesThe Box-Within-a-Box Bifurcations Structure and Its ConsequencesSome Properties of Two-Dimensional Recurrences (Maps)Two-Dimensional Diffeomorphisms and the Foliated Box-Within-a-Box Bifurcations Structureand other papers Readership: Applied mathematicians, engineers and other physicists. Keywords:Endomorphism;Diffeomorphism;Recurrences;Bifurcations Structure