Twist dynamics of vortex interaction in a time-periodic deformation flow

In this paper, we consider a system of vortex interaction in a time-periodic deformation flow. By introducing some new variables, we transform the system into a singular planar system. In polar coordinates, based on a new stability criterion established by the third-order approximation method, we establish sufficient conditions for the existence of twist periodic solution with nonzero angular momentum for the radial equation of the system. Notably, the twist solution is stable in the sense of Lyapunov. Consequently, the singular planar system possesses a periodic solution which is Lyapunov stable in the radial direction.