amplitude equations

SPATIAL-TEMPORAL PATTERNS IN A MULTIDIMENSIONAL ACTIVE MEDIUM FORMED DUE TO POLYMODAL INTERACTION NEAR THE WAVE BIFURCATION

Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out. It is shown that as a result of competition between modes depending on the value of the parameter defining the strength of interaction only two regimes are possible: either quasi one-dimensional travelling waves (there exists only one nonzero mode) or standing waves (al the modes are nonzero).