Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed. (Texts in Applied Mathematics 2) PDF
Preview Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed. (Texts in Applied Mathematics 2)
This edition contains a significant amount of new material. The main rea-
son for this is that the subject of applied dynamical systems theory has
seen explosive growth and expansion throughout the 1990s. Consequently,
a student needs a much larger toolbox today in order to begin research on
significant problems.
I also try to emphasize a broader and more unified point of view. My
goal 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 issues
separately (e.g., dissipative, discrete time, local dynamics; global dynamics
of continuous time conservative systems, etc.). However, in research one
generally needs to have an understanding of each of these areas, and their
inter-relations. For example, in studying a conservative continuous time
system, one might study periodic orbits and their stability by passing to a
Poincar´ e map (discrete time). The question of how stability may be affected
by dissipative perturbations may naturally arise. Passage to the Poincar´ e
map renders the study of periodic orbits a local problem (i.e., they are fixed
points of the Poincar´ e map), but their manifestation in the continuous time
problem may have global implications. An ability to put together a “big
picture” from many (seemingly) disparate pieces of information is crucial
for the successful analysis of nonlinear dynamical systems.
This edition has seen a major restructuring with respect to the first
edition in terms of the organization of the chapters into smaller units with
a single, common theme, and the exercises relevant to each chapter now
being given at the end of the respective chapter.
The bulk of the material in this book can be covered in three ten week
terms. This is an ambitious program, and requires relegating some of the
material to background reading (described below). My goal was to have the
necessary background material side-by-side with the material that I would
lecture on. This tends to be more demanding on the student, but with the
right guidance, it also tends to be more rewarding and lead to a deeper
understanding 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 understanding
of applied dynamical systems theory requires the students to have an inte
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