New Modes of Quasi-Periodic Combustion Near a Degenerate Hopf Bifurcation Point

Steady, planar propagation of a condensed phase reaction front is unstable to disturbances corresponding to pulsating and spinning waves for sufficiently large values of a parameter related to the activation energy. This paper considers the nonlinear evolution equations for the amplitudes of the pulsating and spinning waves in a neighborhood of a double eigenvalue of the problem linearized about the steady, planar solution. In particular, near a degenerate Hopf bifurcation point, closed branches of solutions which represent new quasi-periodic modes of combustion are described.