Discrete Chaos

“The present textbook gives an excellent introduction to this new, and potentially revolutionary, territory. It will take the reader, with clarity and precision, from simple beginnings with 1-dimensional difference equations (and their cascades of period doubling en route to chaos), on to 2- and 3-dimensional systems, and beyond this to fractals and relationships between geometry and dynamics. The final chapter deals with the Julia and Mandelbrot sets, where in my opinion mathematical elegance and pure aesthetic beauty begin to merge.” —From the Foreword, Lord Robert M. May, Department of Zoology, University of Oxford, UK "…the systematic and rigorous exposition on many concepts and results … is very effective for teaching purposes in many kinds of classrooms, both in the framework of theoretical courses and the ones devoted to applications. The main feature of Elaydi’s book is the huge spectrum of examples and exercises … the CD included that contains the program PHASER with several built-in examples as well as a user-friendly environment where the reader can experiment with his or her own examples is quite useful. … a nice guided tour that motivates the reader to a deeper journey into the rich spectrum of properties and applications of dynamical systems and deterministic chaos."—Mathematical Reviews, 2009b“The long-awaited second edition of Discrete Chaos is finally here! Not only is this new edition, with its superb organization and exposition, a delight to read, but the accompanying electronic supplement, including a myriad of insightful computer experiments, is truly engaging. Discrete Chaos can serve as a textbook for undergraduate and beginning graduate courses, as well as a reference for researchers interested in discrete dynamical models. It provides rigorous coverage of stability, bifurcations, and chaos in one- and two-dimensional discrete dynamical systems. The power and the utility of theoretical considerations are successfully demonstrated in numerous problems and significant applications to models from ecology, epidemiology, physics, engineering, and social sciences. Rigorous yet eminently accessible, Discrete Chaos is the most up-to-date book in its class.”—Huseyin Kocak, University of Miami, Florida, USA “One of the features that makes this book unique is that, as a renowned and active researcher in discrete dynamical systems and difference equations, Elaydi integrates very skillfully these two fields, whenever possible, and provides in depth the stability theory for one- and two-dimensional dynamical systems. It is fascinating that, without sacrificing anything important, the author is able to simplify the treatment and compress the material on one-dimensional dynamics into chapter 1 that takes some texts many chapters.” —Danrun Huang, St. Cloud State University, Minnesota, USA"The book under review is an undergraduate-level text. It is a good starting point for scientists and students that would like to move into the field of studying the discrete chaos." – Alexander O. Ignatyev, in Zentralblatt Math, 2009

• Preface. Foreword. The Stability of One-Dimensional Maps.Attraction and Bifurcation. Chaos in One Dimension.Stability of Two-Dimensional Maps.Bifurcation and Chaos in Two Dimensions.Fractals.The Julia and Mandelbrot Sets. Bibliography. Answers to Selected Problems. Index.