Complex Dynamic Behavior on Transition in a Solid Combustion Model

Jun Yu, Department of Mathematics & Statistics, University of Vermont

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. First, a multi-scale weakly nonlinear analysis is used to account for the cumulative effect of small nonlinearities in order to obtain a correct description of the evolution over long times. Numerical solutions are also studied. We show that for special parameters our asymptotic 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.