  We study the Landau model for uniaxial incommensurate-commensurate systems of
the I class by keeping Umklapp terms of third and fourth order in the expansion
of the free energy. It applies to systems in which the soft mode minimum lies
between the corresponding commensurate wave numbers. The minimization of the
Landau functional leads to the sine-Gordon equation with two nonlinear terms,
equivalent to the equation of motion for the well-known classical mechanical
problem of two mixing resonances. We calculate the average free energies for
periodic, quasiperiodic and chaotic solutions of this equation, and show that
in the regime of finite strengths of Umklapp terms only periodic solutions are
absolute minima of the free energy, so that the phase diagram contains only
commensurate configurations. The phase transitions between neighboring
configurations are of the first order, and the wave number of ordering goes
through harmless staircase with a finite number of steps. These results are the
basis for the interpretation of phase diagrams for some materials from the I
class of incommensurate-commensurate systems, in particular of those for
A$_2$BX$_4$ and BCCD compounds. Also, we argue that chaotic barriers which
separate metastable periodic solutions represent an intrinsic mechanism for
observed memory effects and thermal hystereses.
