The existence of multistability in a system with a complex order-parameter equation of the form $\dot{\psi }=y-\psi Q\left({\left|\psi \right|}^2\right)$ is examined, with special reference to optical systems such as multiphoton and multimode lasers. It is shown that the neglect of the phase of the order parameter from the dynamical considerations could lead to a different type of multistable behavior. The general polynomial form of $Q$ for the existence of tristability is obtained.

• Received 21 September 1981

DOI:https://doi.org/10.1103/PhysRevA.26.888