Identification of Intermittent Ordered Patterns as Heteroclinic Connections

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Abstract
Cellular flames stabilized on a porous plug burner at low pressure form ordered patterns consisting of concentric rings of cells. In certain regions of the parameter space of propane-air mixtures, ordered patterns appear intermittently. In these states, patterns of concentric rings persist for varying lengths of time, abruptly dissolve into highly irregular structures with no discernible ring pattern, and then reappear as ordered patterns with the same or slightly different numbers of cells. Experimental evidence and theoretical arguments show that these intermittently ordered states correspond to a network of heteroclinic connections among unstable equilibria.