This edition contains a significant amount of new material. The main rea-son for this is that the subject of applied dynamical systems theory hasseen explosive growth and expansion throughout the 1990s. Consequently,a student needs a much larger toolbox today in order to begin research onsignificant problems.I also try to emphasize a broader and more unified point of view. Mygoal is to treat dissipative and conservative dynamics, discrete and con-tinuous time systems, and local and global behavior, as much as possible,on the same footing. Many textbooks tend to treat most of these issuesseparately (e.g., dissipative, discrete time, local dynamics; global dynamicsof continuous time conservative systems, etc.). However, in research onegenerally needs to have an understanding of each of these areas, and theirinter-relations. For example, in studying a conservative continuous timesystem, one might study periodic orbits and their stability by passing to aPoincar´ e map (discrete time). The question of how stability may be affectedby dissipative perturbations may naturally arise. Passage to the Poincar´ emap renders the study of periodic orbits a local problem (i.e., they are fixedpoints of the Poincar´ e map), but their manifestation in the continuous timeproblem may have global implications. An ability to put together a “bigpicture” from many (seemingly) disparate pieces of information is crucialfor the successful analysis of nonlinear dynamical systems.This edition has seen a major restructuring with respect to the firstedition in terms of the organization of the chapters into smaller units witha single, common theme, and the exercises relevant to each chapter nowbeing given at the end of the respective chapter.The bulk of the material in this book can be covered in three ten weekterms. This is an ambitious program, and requires relegating some of thematerial to background reading (described below). My goal was to have thenecessary background material side-by-side with the material that I wouldlecture on. This tends to be more demanding on the student, but with theright guidance, it also tends to be more rewarding and lead to a deeperunderstanding and appreciation of the subject.The mathematical prerequisites for the course are really not great; ele-mentary analysis, multivariable calculus, and linear algebra are sufficient.In reality, this may not be enough on its own. A successful understandingof applied dynamical systems theory requires the students to have an inte

Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed. (Texts in Applied Mathematics 2) PDF

The list of books you might like