Practical Bifurcation and Stability Analysis

ISBN-13: 9781461425304 / Angielski / Miękka / 2012 / 477 str.

R. Diger U. Seydel

Opis

Fifteen years have elapsed after the second edition of Practical Bifurcation and Stability Analysis was published. During that time period the ?eld of computational bifurcation has become mature. Today, bifurcation mec- nisms are widely accepted as decisive phenomena for explaining and - derstanding stability and structural change. Along with the high level of sophistication that bifurcation analysis has reached, the research on basic computational bifurcation algorithms is essentially completed, at least in - dinary di?erential equations. The focus has been shifting from mathematical foundations towards applications. The evolution from equilibrium to chaos has become commonplace and is no longer at the cutting edge of innovation. But the corresponding methods of practical bifurcation and stability analysis remain indispensable instruments in all applications of mathematics. This constant need for practical bifur- tion and stability analysis has stimulated an e?ort to maintain this book on a present-day level. The author's endeavor has resulted in this third edition. It is based on more than three decades of practical experience with the subject, and on many courses given at several universities.

Recenzje

From the reviews of the third edition:

"The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society

"Methods of practical bifurcation and stability analysis are crucial instruments in applied mathematics. This fact stimulated the author to publish an up-to-date third edition, sixteen years after appearing the second edition. ... The references contain more than 600 items. The excellent presentation of the material will stimulate people in applied sciences to apply the well-prepared instruments." (Klaus R. Schneider, Zentralblatt MATH, Vol. 1195, 2010)

Spis treści

and Prerequisites.- Basic Nonlinear Phenomena.- Applications and Extensions.- Principles of Continuation.- Calculation of the Branching Behavior of Nonlinear Equations.- Calculating Branching Behavior of Boundary-Value Problems.- Stability of Periodic Solutions.- Qualitative Instruments.- Chaos.

Blurb

This book covers the central role that bifurcations play in nonlinear phenomena, explaining mechanisms of how stability is gained or lost. It emphasizes practical and computational methods for analyzing dynamical systems. A wide range of phenomena between equilibrium and chaos is explained and illustrated by examples from science and engineering. The book is a practical guide for performing parameter studies and includes exercises.

Combining an introduction on the textbook level with an exposition of computational methods, this book addresses the mathematical needs of scientists and engineers. It should be of interest to those in a wide variety of disciplines, including physics, mechanical engineering, electrical engineering, chemistry and chemical engineering, biology, and medicine. Both graduate students (in courses on dynamical systems, stability analysis, differential equations, and chaos) and professionals will be able to use the book equally well. The introduction avoids mathematical formalism, and the only required background is calculus.

In the third edition there is a chapter on applications and extensions of standard ODE approaches, for example, to delay equations, to differential-algebraic equations, and to reaction-diffusion problems. Additional material is inserted, including the topics deterministic risk, pattern formation, and control of chaos, and many further references.

Review of Earlier Edition:

"The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society