  In the framework of the Einstein-Dirac-axion-aether theory we consider the
quartet of self-interacting cosmic fields, which includes the dynamic aether,
presented by the unit timelike vector field, the axionic dark mater, described
by the pseudoscalar field, the spinor field associated with fermion particles,
and the gravity field. The key, associated with the mechanism of
self-interaction, is installed into the modified periodic potential of the
pseudoscalar (axion) field constructed on the base of a guiding function, which
depends on one invariant, one pseudo-invariant and two cross-invariants
containing the spinor and vector fields. The total system of the field
equations related to the isotropic homogeneous cosmological model is solved; we
have found the exact solutions for the guiding function for three cases:
nonzero, vanishing and critical values of the cosmological constant. Based on
these solutions, we obtained the expressions for the effective mass of spinor
particles, interacting with the axionic dark matter and dynamic aether. This
effective mass is shown to bear imprints of the cosmological epoch and of the
state of the cosmic dark fluid in that epoch.
