The bifurcation diagram on the left shows the negative peaks of the acoustic velocity as the location of a G-equation flame is varied within a tube. At x_f = 0.3091, these peaks pass through the same point at u_f = -0.27, showing that the solution is periodic. This can be seen clearly in the top-right figure, which shows the power spectral density (PSD) as a function of frequency. As x_f reduces, the system passes through a period-doubling bifurcation, shown by the appearance of two peaks in the bifurcation diagram and a frequency at f/2 in the PDS. A cascade of period-doubling bifurcations ensues, ending up with a chaotic oscillation.
Credit: Karthik Kashinath
Jump to publication (will be at top of next screen)