TY - JOUR
T1 - New modes of quasi-periodic combustion near a degenerate Hopf bifurcation point
AU - Margolis, Stephen B.
AU - Matkowsky, Bernard J.
PY - 1988
Y1 - 1988
N2 - 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.
AB - 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.
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U2 - 10.1137/0148047
DO - 10.1137/0148047
M3 - Article
AN - SCOPUS:0024056673
SN - 0036-1399
VL - 48
SP - 828
EP - 853
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 4
ER -