Dynamics of Cosmological Models with Nonlinear Classical Phantom Scalar Fields. I. Formulation of the Mathematical Model

Mathematical models describing the cosmological evolution of classical and phantom scalar fields with self-action are formulated and analyzed. Systems of dynamical equations in the plane, describing homogeneous cosmological models, have been obtained. It is shown that depending on the parameters of the field model, it is possible to violate the single connection of the phase space of the corresponding dynamical model.