Bursts in oscillatory systems with broken D-4 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 w hen the square symmetry is broken. All possible cycles of this type are ide ntified and the resulting bursts described. Global connections involving fi nite amplitude states are also present. The intricate sequence of bifurcati ons that result is described in several cases. (C)2000 Elsevier Science B.V . All rights reserved.