What is dynamic stability in an induction motor?
If motor has a torque vs. speed capability curve like the curve marked "Fundamental torque" in the image below, the motor, when started, will accelerate to the normal operating point, marked "N," where the motor curve intersects the load curve. That represents normal, stable, steady-state operation.

In some motors, there may be torque harmonics that cause a sharp dip in the motor torque curve as shown by the dashed curve marked as "due to harmonics." In that case, the motor may "crawl" at the point marked "C". If the load momentarily drops a little. The load may accelerate to the point marked "U." That is an unstable operating point because the motor curve is rising above the load curve at that point. The motor could accelerate to load to the normal operating point from that point. Motors are usually designed to prevent harmonic torques of the magnitude shown, so the crawling phenomenon is uncommon.

Motors that have a gentle dip in torque between locked rotor and peak torque are not uncommon. The dashed curve marked "due to double cage or deep bar effects" illustrates that. However the locked rotor torque and the minimum torque, called pull-up torque, are usually sufficiently higher than rated torque to prevent crawling or instability if the motor is sized properly for the load. However those problems could be seen if the load is higher than expected or if the supply voltage is unusually low.