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Berman, G., Strogatz, R., Feinerman, K. (2007). Comparison of a large, new ignition model with laboratory experiments and a state-of-the-art one-step model of thermo-kinetic combustion. Combustion and Flame, 172 (12), 1454-1467. www.thunderstone.com
The nonlinear stability analysis was also carried out. It is demonstrated that the AH bifurcations observed were supercritical. A stable limit cycle emerges as the neutral stability boundary is crossed. In terms of the original problem, this implies that the stable pulsating solutions bifurcate from the travelling solution branches owing to the AH bifurcation. As the activation energy is varied away from the neutral stability boundary, the amplitude of oscillations of the instantaneous flame speed increase and at certain stage the period-doubling bifurcation occurs. It is not clear at the moment what kind of complex dynamical behaviour can be encountered as the bifurcation parameter is further increased and is the focus of future work. It was also demonstrated that the dependence of the flame speed on the activation energy can show the hysteresis type of behaviour. In particular decreasing (or increasing), the activation energy below (or above) the turning point conditions may result in sudden, very abrupt, acceleration (or deceleration) of the flame velocity so that the speed can rapidly change in orders of magnitude in a very short time interval. Such issues may be of practical interest, for example, in fire safety and will be studied in our future work.
The nonlinear stability analysis was also carried out. It is demonstrated that the AH bifurcations observed were supercritical. A stable limit cycle emerges as the neutral stability boundary is crossed. In terms of the original problem, this implies that the stable pulsating solutions bifurcate from the travelling solution branches owing to the AH bifurcation. As the activation energy is varied away from the neutral stability boundary, the amplitude of oscillations of the instantaneous flame speed increase and at certain stage the period-doubling bifurcation occurs. It is not clear at the moment what kind of complex dynamical behaviour can be encountered as the bifurcation parameter is further increased and is the focus of future work. It was also demonstrated that the dependence of the flame speed on the activation energy can show the hysteresis type of behaviour. 81555fee3f1

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