Parametric disorder effects on a subcritical stationary bifurcation

• The cubic–quintic complex Ginzburg–Landau equation with real coefficients has been taken as a model equation with a modulated control parameter.
• In the presence of modulations, the threshold is always negative and lower than for the unmodulated system.
• Above the threshold, the quintic term has profound consequences on the stationary nonlinear solution as well as on the Nusselt number.

For a spatial modulation of the control parameter which describes, for instance, major effects of a rough container boundary in Rayleigh–Bénard convection, the threshold value of the bifurcation from a homogeneous basic state to a spatially periodic state is provided analytically and numerically, taking the one-dimensional cubic–quintic complex Ginzburg–Landau equation with real coefficients as an example. Above the threshold, using the Poincaré–Lindstedt expansion, we show that the quintic term affects both the stationary nonlinear solution and the Nusselt number.