Bursts in oscillatory systems with broken D4 symmetry

A new mechanism responsible for generating regular and irregular bursts of large dynamic range near onset of an oscillatory instability is identified. The bursts are present in systems with nearly square symmetry and are the result of heteroclinic cycles involving infinite amplitude states created when the square symmetry is broken. All possible cycles of this type are identified and the resulting bursts described. Global connections involving finite amplitude states are also present. The intricate sequence of bifurcations that result is described in several cases.