The topological characteristics of the bifurcation and chaos in the motion of combustion fronts in solids

Abstract

We investigate the geometric features in the bifurcation and chaos of a partial differential equation describing the unsteady combustion of solid propellants. Driven by the interaction of the unsteady combustion at the surface and the diffusion inside solids, the motion of the combustion fronts can be steady, harmonically oscillatory, and become more complicated to chaos through a series of bifurcations. We examined the dynamics in both free and forced oscillations. In the free oscillation, by varying a parameter related to the solid property, the intrinsic instability of the combustion is discovered. We find the typical period-doubling to chaos route and verify it via both qualitative and quantitative universalities. In the forced oscillation case, the system is perturbed by an external pressure excitation, leading to a more complicated bifurcation diagram with richer dynamics. Concentrating on the topological characteristics of the periodic orbits, we discover two new types of bifurcation other than the period-doubling bifurcation. In present work, we extract a series subtle topological structures from an infinite-dimensional dynamical systems governed by a partial differential equation with free boundary. We find the results provide an explanation for the period-3 orbits in the experimental data of a full-scale motor.