In this paper, we study the formation of optical bistability (OB) and optical multistability (OM) in a degenerate four-level atomic system by an external magnetic field that is excited by a probe laser field, a coupling laser field and a signal laser field. The coupling field can cause electromagnetically induced transparency (EIT) for the probe field in the atomic medium, while the signal field and/or external magnetic field can switch between single-EIT and two-EIT regimes. Based on these properties, OB and OM effects can be formed at two different frequency regions of the probe field (two channels).
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