Stabilizing steady and periodic behavior in propagating flame fronts

Abstract Propagating flame fronts may exhibit both stable and unstable cellular structures in certain mixtures of fuel and oxidizer. A new algorithm is proposed that allows the stabilization and tracking of steady and oscillatory fronts through a bifurcation sequence that eventually leads to chaotic behaviour. Various states are stabilized by monitoring one experimentally accessible variable and perturbing one boundary condition. No knowledge of the underlying governing equations of the system is required to implement the tracking method. Information about the locations of the unstable steady state and periodic orbits and the magnitudes of the associated eigenvalues and Floquet multipliers is automatically provided by the algorithm.