The Logistic Map and the Route to Chaos

The Logistic Map and the Route to Chaos
Author: Marcel Ausloos
Publisher: Springer Science & Business Media
Total Pages: 413
Release: 2006-02-11
Genre: Science
ISBN: 3540320237

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

The Logistic Map and the Route to Chaos

The Logistic Map and the Route to Chaos
Author: Marcel Ausloos
Publisher: Springer Science & Business Media
Total Pages: 442
Release: 2006-02-10
Genre: Language Arts & Disciplines
ISBN: 9783540283669

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Introduction to Chaos

Introduction to Chaos
Author: H Nagashima
Publisher: CRC Press
Total Pages: 164
Release: 2019-06-06
Genre: Mathematics
ISBN: 0429525656

This book focuses on explaining the fundamentals of the physics and mathematics of chaotic phenomena by studying examples from one-dimensional maps and simple differential equations. It is helpful for postgraduate students and researchers in mathematics, physics and other areas of science.

Introduction to Chaos and Coherence

Introduction to Chaos and Coherence
Author: Jan Froyland
Publisher: Routledge
Total Pages: 145
Release: 2022-01-26
Genre: Science
ISBN: 1351437186

This book provides an introduction to the theory of chaotic systems and demonstrates how chaos and coherence are interwoven in some of the models exhibiting deterministic chaos. It is based on the lecture notes for a short course in dynamical systems theory given at the University of Oslo.

Galileo Unbound

Galileo Unbound
Author: David D. Nolte
Publisher: Oxford University Press
Total Pages: 384
Release: 2018-07-12
Genre: Science
ISBN: 0192528505

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Progress in Optics

Progress in Optics
Author:
Publisher: Elsevier
Total Pages: 455
Release: 1993-05-10
Genre: Science
ISBN: 0080962904

A collection of comprehensive reviews in the field of optics. The first article presents a review of recent investifations concerning multiphoton ionization of atoms in intense radiation fields and includes discussions on above threshold ionization, generation of higher-order harmonics of an intense field interacting with a gaseous medium and the role of chaotic dynamics in the interaction of atoms with monochromatic radiation. A tutorial section on chaotic behaviour is also included. The second article presents a review of modern developments regarding properties of light diffracted by gratings. Both a phemonenological treatment and a macroscopic analysis are presented. The following article reviews developments relating to optical amplifiers, especially those which use semiconductors and optical fibres. The article covers the operating principles, fabrication and performance characteristics. The next article reviews recent research on a promising new class of neural networks, the so-called adaptive multilayer optical networks. Although still in the early states of developments, these devices offer the possibility of implementing optical interconnections in three dimensions and they can be functionally equivalent to several thousand chips. The fifth article deals with idealized but rather useful models of some atomic systems, namely two-level and four-level atoms. The analogy between a quantum two-level atom and a classical model consisting of two coupled optical modes is discussed. Extension of these considerations to optical band structure and to four-level systems is also treated. The concluding article deals thoroughly with free electron lasers in a physical way, while minimum attention is paid to organic generalities and mathematical rigour.

Chaos Theory Tamed

Chaos Theory Tamed
Author: Garnett Williams
Publisher: CRC Press
Total Pages: 518
Release: 1997-09-09
Genre: Mathematics
ISBN: 1482295415

This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.

Bifurcation Control

Bifurcation Control
Author: Guanrong Chen
Publisher: Springer Science & Business Media
Total Pages: 344
Release: 2003-08-26
Genre: Technology & Engineering
ISBN: 9783540403418

Bifurcation control refers to the task of designing a controller that can modify the bifurcation properties of a given nonlinear system, so as to achieve some desirable dynamical behaviors. There exists no similar control theory-oriented book available in the market that is devoted to the subject of bifurcation control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The book is not only aimed at active researchers in the field of bifurcation control and its applications, but also at a general audience in related fields.

Chaos

Chaos
Author: Kathleen Alligood
Publisher: Springer
Total Pages: 620
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642592813

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Chaos in Dynamical Systems

Chaos in Dynamical Systems
Author: Edward Ott
Publisher: Cambridge University Press
Total Pages: 500
Release: 2002-08-22
Genre: Mathematics
ISBN: 9780521010849

Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.