Period doubling and chaotic transient in a model of chain- branching combustion wave propagation by Vladimir Gubernov, Andrei Kolobov, Andrei Polezhaev, Harvinder Sidhu, and Geoffry Mercer Proceedings A Volume ():rspa April 7, 2010 ©2010 by The Royal Society

The dependence of the flame speed, c, on dimensionless activation energy, β, for LA=1 and 10 as shown in figure. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Stability diagrams for LB=1 and r=10−3. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Properties of the Hopf bifurcation. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

(a) Represent the Fourier time series of wmax(t) and (b) show the corresponding Poincaré maps for LA=3, LB=1, r=0.001 and several values of β: (i) 4.08, (ii) , (iii) , (iv) and (v) Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Diagram of period-doubling bifurcations on the, parameter plane for LB=1. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Fine structure of the loci of period-doubling bifurcations on the,, parameter plane for LB=1. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Projection of a strange attractor and route to extinction on the wmax vs ξmax plane plotted for LA=3, LB=1, r=0.001, β= in (a) and β= in (b) respectively. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Lyapunov exponent, σ, as function of β for LA=10, LB=1, r=0.001 and ua=0. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society

Dependence of N on time t for LA=10, LB=1, β= , r=0.001 and ua=0. Vladimir Gubernov et al. Proc. R. Soc. A doi: /rspa ©2010 by The Royal Society