Dynamics of the restricted vortex problem with a honeycomb configuration

Abstract

In this paper, we have investigated the restricted 14-vortex problem with a honeycomb configuration similar to the football surface pattern. First, we give a sufficient condition for the existence of honeycomb configurations and obtain the instability of configurations. Then, we establish the equation of motion of the tracer particle for the restricted 14-vortex problem and analyze the stability and distribution of equilibrium points and singular points. As can be seen from the global phase diagram of system, there are only four types of orbits: equilibrium points, homoclinic orbits, heteroclinic orbits, and periodic orbits.