Principle of pattern selection for nonequilibrium phenomena

A general principle is advanced allowing the classification of nonunique so lutions to nonlinear evolution equations, corresponding to different spatio -temporal patterns. This is done by defining the probability distribution o f patterns, which characterizes multiple solutions as more or less probable with respect to each other. The most probable pattern is naturally defined by the maximum of the pattern distribution. This maximum is shown to be eq uivalent to the minimum of local contraction. The formulated principle play s for nonequilibrium dynamical systems the same ordering role as the condit ion of minimal free energy for equilibrium statistical systems. The general ity of the principle is illustrated by several examples of different nature . (C) 2001 Published by Elsevier Science B.V.