The equivalent circuit of single-phase induction motor is much more complicated, but it is actually based on the T-shaped equivalent circuit, which is a combination of positive sequence circuit and negative sequence circuit.
From the differential equation of the motor, their forms are the same, but from the input quantity, the doubly-fed motor has six input voltages, namely three-phase stator and three-phase rotor, while the single-phase motor has only one input voltage, namely one-phase stator voltage.
This is my understanding of the motor.
Hope to adopt.