Bifurcation analysis on a reactor model with combination of quadratic and cubic steps

In this paper we give a rigorous bifurcation analysis for a reactor model with combination of quadratic and cubic steps. We extend the analysis of Satnoianu et al. in two directions. First, we impose Dirichlet boundary conditions instead of the semi-infinite domain in one space dimension. Second, we consider a variety of different bifurcation phenomena of the corresponding steady state system, focusing on their parametric sensitivity. We show that the system exhibits subcritical pitchfork bifurcation, supercritical pitchfork bifurcation and transcritical bifurcation in the different regimes of control parameters. To compare the decades old work by Auchmuty et al., we show that the spatial structures formed by the parameter p ∈ [0, 1] are richer than those formed by the purely quadratic step for p = 0 and the purely cubic step for p = 1 respectively.