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Author: Bai-lin Hao Publisher: World Scientific ISBN: 9789971503628 Category : Science Languages : en Pages : 402
Book Description
Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.
Author: Bai-lin Hao Publisher: World Scientific ISBN: 9789971503628 Category : Science Languages : en Pages : 402
Book Description
Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.
Author: Bailin Hao Publisher: World Scientific ISBN: 9814513717 Category : Science Languages : en Pages : 367
Book Description
This volume, the first of a two-volume book, consists of a collection of comprehensive reviews and lectures written by active researchers on topics in chaotic phenomena.
Author: Hao Bailin Publisher: World Scientific ISBN: 9813236442 Category : Science Languages : en Pages : 520
Book Description
Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps
Author: Bailin Hao Publisher: World Scientific ISBN: 9814513725 Category : Science Languages : en Pages : 400
Book Description
Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.
Author: Kathleen Alligood Publisher: Springer ISBN: 3642592813 Category : Mathematics Languages : en Pages : 620
Book Description
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.
Author: Bharathwaj Muthuswamy Publisher: Springer ISBN: 331918105X Category : Technology & Engineering Languages : en Pages : 234
Book Description
The purpose of this introductory book is to couple the teaching of chaotic circuit and systems theory with the use of field programmable gate arrays (FPGAs). As such, it differs from other texts on chaos: first, it puts emphasis on combining theoretical methods, simulation tools and physical realization to help the reader gain an intuitive understanding of the properties of chaotic systems. Second, the "medium" used for physical realization is the FPGA. These devices are massively parallel architectures that can be configured to realize a variety of logic functions. Hence, FPGAs can be configured to emulate systems of differential equations. Nevertheless maximizing the capabilities of an FPGA requires the user to understand the underlying hardware and also FPGA design software. This is achieved by the third distinctive feature of this book: a lab component in each chapter. Here, readers are asked to experiment with computer simulations and FPGA designs, to further their understanding of concepts covered in the book. This text is intended for graduate students in science and engineering interested in exploring implementation of nonlinear dynamical (chaotic) systems on FPGAs.
Author: Bai-lin Hao
Author: Bai-lin Hao
Author: Bailin Hao
Author: Hao Bailin
Author: Bailin Hao
Author: 
Author: Hao Bai-lin
Author: Bailin Hao
Author: Marcel Ausloos
Author: Kathleen Alligood
Author: Bharathwaj Muthuswamy