Bursts

摘要

A thorough understanding of imperfections is critical for many engineering applications. At the linear level, local imperfections can trap modes and be responsible for a new class of potential instabilities. At the weakly nonlinear level, imperfections are known to play an important role near degeneracies in parameter space. Nominally symmetric systems are always degenerate in this sense since the presence of symmetries typically eliminates certain terms from the amplitude equations describing the evolution of instabilities in such systems. Consequently, such systems are almost always sensitive to small symmetry-breaking imperfections. Particularly dangerous are imperfections that destroy continuous symmetries, such as translation or rotation invariance. Such imperfections are typically responsible for the introduction of global bifurcations into the dynamics, and these are likely to be responsible for the appearance of chaos in the imperfect system (Knobloch 1996). However, in certain cases the loss of discrete symmetry can have a similar effect, at least if the symmetry group is large enough. This is the case in the class of system discussed below.