The Intermittent States

Intermittent states are observed whenever an ordered pattern appears at irregular intervals of time. Some of the intermittent states are associated with heteroclinic connections.

In the 9/3-4HC intermittent state an ordered pattern of nine outer cells and three inner cells appears for varying lengths of time, mostly for short times (10 frames) but occasionally for long times (120 frames). All of the ordered patterns are unstable and the resulting dynamics appears because the system trajectory is attracted to then repelled from unstable equilibria. Other ordered patterns (such as the nine around four) also can be observed. At times in between the ordered patterns the flame has a highly irregular spatiotemporal structure with no discernible pattern of concentric rings. The HC states correspond to a network of heteroclinic connections among unstable equilibria.

In the 9/2U Intermittent State, two cells (around a point) are unstable. There is no parameter at which two cells can be stabilized. Two cells, two cells surrounded by one ring, two cells surrounded by two rings--in each case the two cells decay to a single cell or to three cells. The chaotic dynamics of the ordered states then kicks the system out of the one cell and three cell patterns so that the system is constantly moving among these three states.

9/3-4H Movie (.95M)

9/2U Movie (.44M)

Related Papers:

• Identification of Intermittent Ordered Patterns as Heteroclinic Connections
  E. Stone, M. Gorman, M. el-Hamdi and K. A. Robbins (1996)
  Physical Review letters 76 2061-2064.