Intermittency Near a codimension Three Steady-State bifurcation

We study the existence and stability of heteroclinic connections near “hopping” cellular flame patterns. These are dynamic patterns in which individual cells make sequential, and abrupt, changes in their angular positions while they rotate nonuniformly about the center of a circular domain. Normal form analysis and experimental works have shown that these patterns are associated with a homoclinic cycle connecting group related equilibria. In fact, they emerge through a codimension three steady-state bifurcation of three modes with wave numbers in a 2:3:4 ratio. While cycles are known to exist in the mode-2 and mode-4 interactions, here we show that mode-3 destabilizes the connection so that only remnants, i.e. intermittent flame patterns of the cycles can be observed.