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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.

Phase transformations (Statistical physics) --- Condensed matter. --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Mathematics. --- Partial differential equations. --- System theory. --- Fluids. --- Partial Differential Equations. --- Fluid- and Aerodynamics. --- Complex Systems. --- Liquids --- Matter --- Solids --- Phase rule and equilibrium --- Statistical physics --- Differential equations, partial. --- Partial differential equations --- Systems, Theory of --- Systems science --- Science --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Philosophy