Spatiotemporal dynamics of flame front instability described by an extended Kuramoto-Sivashinsky equation

We numerically study the spatiotemporal dynamics in an extended Kuramoto-Sivashinsky equation describing a freely propagating flame in a Hele-Shaw cell. The spatiotemporal dynamics of flame front undergoes a significant transition from low-dimensional to high-dimensional deterministic chaos with increasing the Rayleigh number. This is clearly identified by the permutation spectrum and the multiscale complexity-entropy causality plane. The Shannon entropy incorporating the probability of the degree in the interface network is useful for capturing the significant changes in randomness in the spatiotemporal dynamics.