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.
This second edition introduces a unified theory for topological phase
transitions, provides a first-principle approach to statistical and
quantum physics, and offers a microscopic mechanism of quantum
condensates (Bose-Einstein condensation, superfluidity, and
superconductivity).
Reviews of first edition:
"The goals of this interesting book are to derive a general principle of
dynamic transitions for dissipative systems and to establish a
systematic dynamic transition theory for a wide range of problems in the
nonlinear sciences. ... The intended audience for this book includes
students and researchers working on nonlinear problems in physics,
meteorology, oceanography, biology, chemistry, and the social sciences."
(Carlo Bianca, Mathematical Reviews, December, 2014)
"This is a clearly written book on numerous types of phase transitions
taken in a broad sense when a dynamical dissipative system transforms
from one physical state into another. ... The book is a very useful
literature not only for the professionals in the field of dynamic
systems and phase transitions but also for graduate students due to its
interdisciplinary coverage and state-of-the-art level." (Vladimir Čadez,
zbMATH, Vol. 1285, 2014)
