Secondary cycle of equilibria in a system with cosymmetry,its creation by bifurcation and impossibility of symmetric treatment of it

A study is reported of the bifurcation of a cycle of equilibria of an autonomous differential equation with cosymmetry in Hilbert space, which is a simulation of the problem of planar filtrational convection of a fluid in a porous medium. The Lyapunov-Schmidt method and perturbation theory are used to find its amplitude and the damping rate of the dominant mode. It is shown that, in the abstract general model, and also in the problem of convection in a rectangular container, this damping rate varies along the cycle of equilibria. Hence, the cycle of equilibria cannot be an orbit of the action of any symmetry group of the given system. (c) 1995 American Institute of Physics.