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In the framework of the Einstein-Maxwell-aether-axion theory we consider theself-consistent model based on the concept of a two-level control, which iscarried out by the dynamic aether over the behavior of the axionically activeelectrodynamic system. The Lagrangian of this model contains two guidingfunctions, which depend on four differential invariants of the aether velocity:the scalar of expansion of the aether flow, the square of the accelerationfour-vector, the squares of the shear and vorticity tensors. The guidingfunction of the first type is an element of the effective aetheric metric; thiseffective metric is involved in the formulation of kinetic terms for thevector, pseudoscalar and electromagnetic fields and predetermines features oftheir evolution. The guiding function of the second type is associated with thedistribution of axions and describes its vacuum average value; basically, thisfunction appears in the potential of the axion field and predetermines theposition and depth of its minima. The self-consistent set of coupled masterequations of the model is derived. The example of the static sphericallysymmetric system is considered as an application.

The extended Einstein-Maxwell-aether-axion theory: Effective metric as an instrument of the aetheric control over the axion dynamics