Dynamics of a restricted (6 + 1)-vortex problem

Abstract

Abstract This paper investigates the dynamics of a restricted (6 + 1)-vortex problem. The existence of nested equilateral triangle configurations depends on the position of two triangles, which can be divided into two situations: staggered arrangement and symmetrical arrangement. Firstly, we provide the existence conditions for the configuration and further discuss the stability of the configuration numerically. Secondly, we have established the global dynamics of the restricted point-vortex problem with configurations under different arrangements, including the dynamic behavior of equilibrium points, periodic orbits, homoclinic orbits, and heteroclinic orbits.