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Books > Science & Mathematics > Mathematics > Applied mathematics > Chaos theory

Chaos, Criminology, and Social Justice - The New Orderly (Dis)Order (Hardcover): Dragan Milovanovic Chaos, Criminology, and Social Justice - The New Orderly (Dis)Order (Hardcover)
Dragan Milovanovic
R2,917 Discovery Miles 29 170 Ships in 10 - 15 working days

Chaos theory challenges the presumption that the cosmos is orderly, linear, and predictable-but it does not imply pure randomness and chance events. Rather, chaos-informed postmodernist analysis introduces a new vision by celebrating unexpected, surprise, ironic, contradictory, and emergent elements. Scholars in many disciplines are taking this perspective as an alternative to the entrenched structural functionalism and empiricism rooted in linear science. In the early 1990s studies began to emerge applying chaos theory to criminology, law, and social change. This book brings together some of the key thinkers in these areas. Part I situates chaos theory as a constitutive thread in contemporary critical thought in criminology and law. It seeks to provide the reader with a sensitivity to how chaos theory fits within the postmodern perspective and an understanding of its conceptual tools. Part II comprises chapters on applying the chaos perspective to critical criminology and law and, beyond, to peacemaking. Part III presents studies in chaos-informed perspectives on new social movement theory, social change, and the development of social justice. While the book emphasizes the usefulness of the conceptual tools of chaos theory in critical criminology and law, its ultimate goal goes beyond theory-building to provide vistas for understanding the contemporary social scene and for the development of the new just society.

A Random Walk in Physics - Beyond Black Holes and Time-Travels (Hardcover, 1st ed. 2021): Massimo Cencini, Andrea Puglisi,... A Random Walk in Physics - Beyond Black Holes and Time-Travels (Hardcover, 1st ed. 2021)
Massimo Cencini, Andrea Puglisi, Davide Vergni, Angelo Vulpiani
R1,276 Discovery Miles 12 760 Ships in 12 - 17 working days

This book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.

Differential Equations in Engineering - Research and Applications (Hardcover): Nupur Goyal, Piotr Kulczycki, Mangey Ram Differential Equations in Engineering - Research and Applications (Hardcover)
Nupur Goyal, Piotr Kulczycki, Mangey Ram
R4,566 Discovery Miles 45 660 Ships in 12 - 17 working days

Focuses on the latest research in the field of differential equations in engineering applications Discusses the most recent research findings that are occurring across different institutions Identifies the gaps in the knowledge of differential equations Presents the most fruitful areas for further research in advanced processes Offers the most forthcoming studies in modeling and simulation along with real-world case studies

Introduction to Discrete Dynamical Systems (Hardcover): M. Martelli Introduction to Discrete Dynamical Systems (Hardcover)
M. Martelli
R5,331 Discovery Miles 53 310 Ships in 10 - 15 working days

A timely, accessible introduction to the mathematics of chaos

The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized.

Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks.

An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author’s 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

Complexity And Control: Towards A Rigorous Behavioral Theory Of Complex Dynamical Systems (Hardcover): Vladimir G. Ivancevic,... Complexity And Control: Towards A Rigorous Behavioral Theory Of Complex Dynamical Systems (Hardcover)
Vladimir G. Ivancevic, Darryn J Reid
R6,032 Discovery Miles 60 320 Ships in 10 - 15 working days

The book Complexity and Control: Towards a Rigorous Behavioral Theory of Complex Dynamical Systems is a graduate-level monographic textbook, intended to be a novel and rigorous contribution to modern Complexity Theory.This book contains 11 chapters and is designed as a one-semester course for engineers, applied and pure mathematicians, theoretical and experimental physicists, computer and economic scientists, theoretical chemists and biologists, as well as all mathematically educated scientists and students, both in industry and academia, interested in predicting and controlling complex dynamical systems of arbitrary nature.

Chaos, Complexity And Transport - Proceedings Of The Cct '15 (Hardcover): Gwenn Boedec, Christophe Eloy, Xavier Leoncini Chaos, Complexity And Transport - Proceedings Of The Cct '15 (Hardcover)
Gwenn Boedec, Christophe Eloy, Xavier Leoncini
R3,883 Discovery Miles 38 830 Ships in 12 - 17 working days

The main goal is to offer to readers a panorama of recent progress in nonlinear physics, complexity and transport with attractive chapters readable by a broad audience. It allows to gain an insight into these active fields of research and notably promotes the interdisciplinary studies from mathematics to experimental physics. To reach this aim, the book collects a selection of contributions to the third edition of the CCT conference (Marseilles, 1-5 June 2015).

Resonance And Bifurcation To Chaos In Pendulum (Hardcover): Albert C.J. Luo Resonance And Bifurcation To Chaos In Pendulum (Hardcover)
Albert C.J. Luo
R2,731 Discovery Miles 27 310 Ships in 10 - 15 working days

A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system.This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.

Stochastic Dynamics Of Complex Systems: From Glasses To Evolution (Hardcover, New): Henrik Jeldtoft Jensen, Paolo Sibani Stochastic Dynamics Of Complex Systems: From Glasses To Evolution (Hardcover, New)
Henrik Jeldtoft Jensen, Paolo Sibani
R2,420 Discovery Miles 24 200 Ships in 12 - 17 working days

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex - for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways.The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques.This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now.

Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott (Hardcover): William Graham... Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott (Hardcover)
William Graham Hoover, Carol Griswold Hoover
R2,118 Discovery Miles 21 180 Ships in 12 - 17 working days

This book aims to provide a lively working knowledge of the thermodynamic control of microscopic simulations, while summarizing the historical development of the subject, along with some personal reminiscences. Many computational examples are described so that they are well-suited to learning by doing. The contents enhance the current understanding of the reversibility paradox and are accessible to advanced undergraduates and researchers in physics, computation, and irreversible thermodynamics.

Dynamical Systems - Theories and Applications (Paperback): Zeraoulia Elhadj Dynamical Systems - Theories and Applications (Paperback)
Zeraoulia Elhadj
R1,610 Discovery Miles 16 100 Ships in 12 - 17 working days

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.

Laws of Chaos - Invariant Measures and Dynamical Systems in One Dimension (Hardcover, 1997 ed.): Abraham Boyarsky, Pawel Gora Laws of Chaos - Invariant Measures and Dynamical Systems in One Dimension (Hardcover, 1997 ed.)
Abraham Boyarsky, Pawel Gora
R3,274 Discovery Miles 32 740 Ships in 10 - 15 working days

A hundred years ago it became known that deterministic systems can exhibit very complex behavior. By proving that ordinary differential equations can exhibit strange behavior, Poincare undermined the founda tions of Newtonian physics and opened a window to the modern theory of nonlinear dynamics and chaos. Although in the 1930s and 1940s strange behavior was observed in many physical systems, the notion that this phenomenon was inherent in deterministic systems was never suggested. Even with the powerful results of S. Smale in the 1960s, complicated be havior of deterministic systems remained no more than a mathematical curiosity. Not until the late 1970s, with the advent of fast and cheap comput ers, was it recognized that chaotic behavior was prevalent in almost all domains of science and technology. Smale horseshoes began appearing in many scientific fields. In 1971, the phrase 'strange attractor' was coined to describe complicated long-term behavior of deterministic systems, and the term quickly became a paradigm of nonlinear dynamics. The tools needed to study chaotic phenomena are entirely different from those used to study periodic or quasi-periodic systems; these tools are analytic and measure-theoretic rather than geometric. For example, in throwing a die, we can study the limiting behavior of the system by viewing the long-term behavior of individual orbits. This would reveal incomprehensibly complex behavior. Or we can shift our perspective: Instead of viewing the long-term outcomes themselves, we can view the probabilities of these outcomes. This is the measure-theoretic approach taken in this book."

Deterministic Chaos In One Dimensional Continuous Systems (Hardcover): Jan Awrejcewicz, Vadim A. Krysko, Irina V Papkova, Anton... Deterministic Chaos In One Dimensional Continuous Systems (Hardcover)
Jan Awrejcewicz, Vadim A. Krysko, Irina V Papkova, Anton V. Krys'ko
R5,644 Discovery Miles 56 440 Ships in 10 - 15 working days

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.

Complex Systems: Chaos and Beyond - A Constructive Approach with Applications in Life Sciences (Hardcover, 2001 ed.): Kunihiko... Complex Systems: Chaos and Beyond - A Constructive Approach with Applications in Life Sciences (Hardcover, 2001 ed.)
Kunihiko Kaneko, Ichiro Tsuda
R3,193 Discovery Miles 31 930 Ships in 10 - 15 working days

Chaos in science has always been a fascinating realm since it challenges the usual scientific approach of reductionism. While carefully distinguishing between complexity, holism, randomness, incompleteness, nondeterminism and stochastic behaviour the authors show that, although many aspects of chaos have been phenomenologically understood, most of its defining principles are still difficult to grasp and formulate. Demonstrating that chaos escapes all traditional methods of description, the authors set out to find new methods to deal with this phenomenon and illustrate their constructive approach with many examples from physics, biology and information technology. While maintaining a high level of rigour, an overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the specialist level, to a wider interdisciplinary readership.

Instabilities, Chaos And Turbulence (2nd Edition) (Hardcover, 2nd Revised edition): Paul Manneville Instabilities, Chaos And Turbulence (2nd Edition) (Hardcover, 2nd Revised edition)
Paul Manneville
R3,317 Discovery Miles 33 170 Ships in 12 - 17 working days

This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Chaos and Order in the Capital Markets (Hardcover, 2Rev ed): Edgar E. Peters Chaos and Order in the Capital Markets (Hardcover, 2Rev ed)
Edgar E. Peters
R2,200 R1,763 Discovery Miles 17 630 Save R437 (20%) Ships in 10 - 15 working days

The latest developments in chaos theory — from an industry expert

Chaos and Order in the Capital Markets was the first book to introduce and popularize chaos as it applies to finance. It has since become the classic source on the topic. This new edition is completely updated to include the latest ripples in chaos theory with new chapters that tie in today's hot innovations, such as fuzzy logic, neural nets, and artificial intelligence.

Critical praise for Peters and the first edition of Chaos and Order in the Capital Markets

"The bible of market chaologists." — BusinessWeek

"Ed Peters has written a first-class summary suitable for any investment professional or skilled investor." — Technical Analysis of Stocks & Commodities

"It ranks among the most provocative financial books of the past few years. Reading this book will provide a generous payback for the time and mental energy expended." — Financial Analysts Journal

This second edition of Chaos and Order in the Capital Markets brings the topic completely up to date with timely examples from today's markets and descriptions of the latest wave of technology, including genetic algorithms, wavelets, and complexity theory.

Chaos and Order in the Capital Markets was the very first book to explore and popularize chaos theory as it applies to finance. It has since become the industry standard, and is regarded as the definitive source to which analysts, investors, and traders turn for a comprehensive overview of chaos theory. Now, this invaluable reference — touted by BusinessWeek as "the bible of market chaologists" — has been updated and revised to bring you the latest developments in the field.

Mainstream capital market theory is based on efficient market assumptions, even though the markets themselves exhibit characteristics that are symptomatic of nonlinear dynamic systems. As it explores — and validates — this nonlinear nature, Chaos and Order repudiates the "random walk" theory and econometrics. It shifts the focus away from the concept of efficient markets toward a more general view of the forces underlying the capital market system.

Presenting new analytical techniques, as well as reexamining methods that have been in use for the past forty years, Chaos and Order offers a thorough examination of chaos theory and fractals as applied to investments and economics. This new edition includes timely examples from today's markets and descriptions of cutting-edge technologies-genetic algorithms, wavelets, complexity theory-and hot innovations, such as fuzzy logic and artificial intelligence.

Beyond the history of current capital market theory, Chaos and Order covers the crucial characteristics of fractals, the analysis of fractal time series through rescaled range analysis (R/S), the specifics of fractal statistics, and the definition and analysis of chaotic systems. It offers an in-depth exploration of:

  • Random walks and efficient markets — the development of the efficient market hypothesis (EMH) and modern portfolio theory
  • The linear paradigm — why it has failed
  • Nonlinear dynamic systems — phase space, the Henon Map, Lyapunov exponents
  • Applying chaos and nonlinear methods — neural networks, genetic algorithms
  • Dynamical analysis of time series — reconstructing a phase space, the fractal dimension

Tonis Vaga's Coherent Market Hypothesis — the theory of social imitation, control parameters, Vaga's implementations

Plus, Chaos and Order now contains a Windows-compatible disk including data sets for running analyses described in the appendices.

Written by a leading expert in the field, Chaos and Order in the Capital Markets has all the information you need for a complete, up-to-date look at chaos theory. This latest edition will undoubtedly prove to be as invaluable as the first.

Physics Of Chaos In Hamiltonian Systems, The (2nd Edition) (Hardcover, 2nd Revised edition): George Zaslavsky Physics Of Chaos In Hamiltonian Systems, The (2nd Edition) (Hardcover, 2nd Revised edition)
George Zaslavsky
R3,407 Discovery Miles 34 070 Ships in 12 - 17 working days

This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincare recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries.This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion.The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students.

Generating Families in the Restricted Three-Body Problem (Hardcover, 1997 ed.): Michel Henon Generating Families in the Restricted Three-Body Problem (Hardcover, 1997 ed.)
Michel Henon
R3,278 Discovery Miles 32 780 Ships in 12 - 17 working days

The classical three-body problem is of great importance for its applications to astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which a large number have been computed numerically. Here the author explains and organizes this material through a systematic study of generating families, which are the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. The most critical part is the study of bifurcations. Many cases are distinguished and studied separately and detailed recipies are given. Their use is illustrated by determining generating families, and comparing them with numerical computations for the Earth+Moon and Sun-Jupiter systems.

Bifurcations In Piecewise-smooth Continuous Systems (Hardcover): David John Warwick Simpson Bifurcations In Piecewise-smooth Continuous Systems (Hardcover)
David John Warwick Simpson
R3,213 Discovery Miles 32 130 Ships in 12 - 17 working days

Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail.

NeimarkSacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

Chaos, Noise and Fractals (Paperback): E. Roy Pike, L.A. Lugiato Chaos, Noise and Fractals (Paperback)
E. Roy Pike, L.A. Lugiato
R2,080 Discovery Miles 20 800 Ships in 12 - 17 working days

The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Introduction To Mathematical Billiards, An (Hardcover): Utkir A. Rozikov Introduction To Mathematical Billiards, An (Hardcover)
Utkir A. Rozikov
R2,730 Discovery Miles 27 300 Ships in 10 - 15 working days

'This book offers one of the few places where a collection of results from the literature can be found ... The book has an extensive bibliography ... It is very nice to have the compendium of results that is presented here.'zbMATHA mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.

Nonlinearity, Chaos, and Complexity - The Dynamics of Natural and Social Systems (Hardcover): Cristoforo Sergio Bertuglia,... Nonlinearity, Chaos, and Complexity - The Dynamics of Natural and Social Systems (Hardcover)
Cristoforo Sergio Bertuglia, Franco Vaio
R6,939 Discovery Miles 69 390 Ships in 12 - 17 working days

Covering a broad range of topics, this text provides a comprehensive survey of the modeling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this a unique text in the midst of many current books on chaos and complexity. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.

2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach (Hardcover): Zeraoulia Elhadj, Julien Clinton Sprott 2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach (Hardcover)
Zeraoulia Elhadj, Julien Clinton Sprott
R3,439 Discovery Miles 34 390 Ships in 12 - 17 working days

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 H non 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 H non 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.

Frontiers In The Study Of Chaotic Dynamical Systems With Open Problems (Hardcover): Julien Clinton Sprott, Zeraoulia Elhadj Frontiers In The Study Of Chaotic Dynamical Systems With Open Problems (Hardcover)
Julien Clinton Sprott, Zeraoulia Elhadj
R2,940 Discovery Miles 29 400 Ships in 12 - 17 working days

This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.

Dynamical Systems - Stability, Symbolic Dynamics, and Chaos (Hardcover, 2nd edition): Clark Robinson Dynamical Systems - Stability, Symbolic Dynamics, and Chaos (Hardcover, 2nd edition)
Clark Robinson
R5,876 Discovery Miles 58 760 Ships in 9 - 15 working days

Several distinctive aspects make Dynamical Systems unique, including:
o treating the subject from a mathematical perspective with the proofs of most of the results included
o providing a careful review of background materials
o introducing ideas through examples and at a level accessible to a beginning graduate student
o focusing on multidimensional systems of real variables

The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.

Recent Progress In Controlling Chaos (Hardcover): Miguel A.F. Sanjuan, Celso Grebogi Recent Progress In Controlling Chaos (Hardcover)
Miguel A.F. Sanjuan, Celso Grebogi
R4,243 Discovery Miles 42 430 Ships in 12 - 17 working days

This review volume consists an indispensable collection of research papers chronicling the recent progress in controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to as turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics.Recent Progress in Controlling Chaos provides an excellent broad overview of the subject matter, and will be especially useful for graduate students, researchers and scientists working in the areas of nonlinear dynamics, chaos and complex systems. The authors, world-renowned scientists and prominent experts in the field of controlling chaos, will offer readers through their research works, a fascinating insight into the state-of-the-art technology used in the progress in key techniques and concepts in the field of control.

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