The dynamics of a cosmological model fueled by scalar field dark matter with a cosh-like potential plus a cosmological constant is investigated in detail. It is revealed that the late-time attractor is always the de Sitter solution, and that, depending on the values of the free parameters, the oscillating solution of the scalar field -- modeling cold dark matter -- mediates between some early stage (say, the radiation-dominated solution) and the accelerating de Sitter attractor.
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