Amplitude equations for the onset of convection in a reactive mixture in a porous medium

Amplitude equations near the onset of both the stationary and the oscillatory instability in a binary mixture (of miscible fluids) with fast chemical reaction in a porous medium are derived. A forward bifurcation for stationary convection and both forward and inverse bifurcations for oscillatory convection, depending on the value of some characteristic parameters, are predicted. The system also studied exhibits, in a certain parameter range for the oscillatory onset, nonlinear focusing phenomena which lead, together with the always present dissipation, to spatially and temporally irregular behavior near threshold. The competition between dispersive tendencies and damping can give rise to this complex structure even for initially small perturbations.