Transitions and families of steady states in Darcy convection

We consider selection of equilibria in the problem of thermal convection of incompressible fluid in a porous medium (the Darcy model). V. Yudovich (1991) explained that given equations possess with nontrivial cosymmetry which implies the appearance of a continuous family of equilibria. The stability spectrum in this system is not constant along the family of steady states and it leads to the interesting bifurcations and dynamics. Selection of steady states under different perturbations is studied via computer experiment based on the finite-difference approach