This book is an introduction to a comprehensive and unified dynamic
transition theory for dissipative systems and to applications of the
theory to a range of problems in the nonlinear sciences. The main
objectives of this book are to introduce a general principle of dynamic
transitions for dissipative systems, to establish a systematic dynamic
transition theory, and to explore the physical implications of
applications of the theory to a range of problems in the nonlinear
sciences. The basic philosophy of the theory is to search for a complete
set of transition states, and the general principle states that dynamic
transitions of all dissipative systems can be classified into three
categories: continuous, catastrophic and random. The audience for this
book includes advanced graduate students and researchers in mathematics
and physics as well as in other related fields.