Analysing instability of combustion waves using the Evans function

Jason Sharples, Harvi Sidhu, Vladimir Gubernov


We consider travelling wave solutions of a reaction-diffusion system corresponding to a single step, homogeneous, premixed combustion scheme with Newtonian heat loss and general Lewis number. Particular attention is paid to unstable combustion wave regimes, especially those associated with oscillatory behaviour. The instability analysis is conducted with the use of Evans function techniques, which we use to derive eigenvalues of the linear stability problem via the argument principle and Nyquist plots. These techniques permit the study of transitions to different modes of unstable behaviour in great detail. Threshold values of the parameters corresponding to Hopf and Bogdanov--Takens bifurcation are established and it is shown that for certain parameter values the system exhibits a period doubling route to chaotic behaviour.

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combustion wave; stability; Evans function; argument principle

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