Limit cycles for a class of eleventh $\mathbb{Z}_{12}-$equivariant systems without infinite critical points

Abstract

We analyze the complex dynamics dynamics of a family of $\mathbb{Z}_{12}-$equivariant planar systems, by using their reduction to an Abel equation. We derive conditions in the parameter space that allow uniqueness and hyperbolicity of a limit cycle surrounding either $1,~13$ or $25$ equilibria.