Complex dynamic behavior on transition in a solid combustion model
University of Vermont
University of Akron
University of Maryland (Future Affiliation: University of Vermont)
Last modified: August 15, 2006
Through examples in a free-boundary model of solid combustion, this study concerns nonlinear transition behavior of small disturbances of front propagation and temperature as they evolve in time. This includes complex dynamics of period doubling and quadrupling, and it eventually leads to chaotic oscillations. The mathematical problem is interesting as solutions to the linearized equations are unstable when a bifurcation parameter related to the activation energy passes through a critical value. Therefore, it is crucial to account for the cumulative effect of small nonlinearities to obtain a correct description of the evolution over long times. Both asymptotic and numerical solutions are studied. We show that for special parameters our method with some dominant modes captures the formation of coherent structures. Weakly nonlinear analysis for a general case is difficult due to the complex dynamics of the problem which leads to chaos and we discuss possible methods to improve our prediction of the solutions in the chaotic case.