Essential Elements of Nonlinearity, Bifurcation And Chaos Theory

This book focuses on introducing both theoretical and application oriented approaches in science and engineering. It is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.

Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.

This book attempts to present some current research progress and results on the interplay of fuzzy logic and chaos theory.

This book attempts to present some current research progress and results on the interplay of fuzzy logic and chaos theory. More specifically, this book includes a collections of some state-of-the-art surveys, tutorials, and application examples written by some experts working in the interdisciplinary fields overlapping fuzzy logic and chaos theory. The content of the book covers fuzzy definition of chaos, fuzzy modeling and control of chaotic systems using both Mamdani and Takagi-Sugeno models, fuzzy model identification using genetic algorithms and neural network schemes, bifurcation phenomena and self-referencing in fuzzy systems, complex fuzzy systems and their collective behaviours, as well as some applications of combining fuzzy logic and chaotic dynamics, such as fuzzy-chaos hybrid controllers for nonlinear dynamic systems, and fuzzy-model-based chaotic cryptosystems. This book can serve as a handy reference for researchers working in the interdisciplines related, among others, to both fuzzy logic and chaos theory.

The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics.

The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set theory and then an in?nite-valued logic of Lot?

The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set theory and then an in?nite-valued logic of Lot? A. Zadeh were so c- fusing that they were called fuzzy set theory and fuzzy logic; a deterministic system found by E. N. Lorenz to have random behaviours was so unusual that it was lately named a chaotic system. Just like irrational and imaginary numbers, negative energy, anti-matter, etc.,