  In this work we suggest (in a formal analogy with Linde chaotic inflation
scenario) simple dynamical model of the dark energy or cosmological constant.
Concretely, we suggest a Lagrangian dependent of Universe scale factor and
scalar field (with constant and positive total energy density as cosmological
constant). Then, Euler-Lagrange equation for Universe scale factor is
equivalent to the second Friedman equation for the flat empty space with
cosmological constant (in this sense our model is full agreement with recent
astronomical observations). Also there is Euler-Lagrange equation for scalar
field that includes additional "friction" term and negative first partial
derivative of unknown potential energy density (this equation is, in some way,
similar to Klein-Gordon equation modified for cosmic expansion in Linde chaotic
inflation scenario). Finally, total time derivative of the (constant) scalar
field total energy density must be zero. It implies third dynamical equation
which is equivalent to usual Euler-Lagrange equation with positive partial
derivative of unknown potential energy density (this equation is formally
exactly equivalent to corresponding equation in static Universe). Last two
equations admit simple exact determination of scalar field and potential energy
density, while cosmological constant stands a "free parameter". Potential
energy density represents a square function of scalar field with unique maximum
(dynamically non-stable point). Any initial scalar field tends
(co-exponentially) during time toward the same final scalar field, argument of
the maximum of the potential energy density. It admits a possibility that final
dynamically non-stable scalar field value turns out spontaneously in any other
scalar field value when all begins again (like Sisyphus boulder motion).
