The various phenomena discussed in the preceding chapters are among the large number of problems described by systems of nonlinear differential equations which depend on one or more control parameters (e.g., the temperature gradient across the boundaries of a Rayleigh-Bénard cell, the angular velocity of the cylinders of a Taylor-Couette apparatus, the concentration of some reactive species in chemically active media, etc.). When studying these problems, one often wishes to know what are the fixed points of the dynamics, their stability, and their dependence on the control parameters. Furthermore, since multistability easily occurs in these systems, it is important to know, for practical purposes, how and why a particular state may be selected. The basic concepts that are needed to answer these questions and that are at the origin of the methods used throughout this book will be summarized here.
KeywordsCombustion Vortex Anisotropy Convection Manifold
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