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

preprint2016arXivOpen access

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.

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

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Limit cycles for a class of eleventh Z12−\mathbb{Z}_{12}-Z12​−equivariant systems without infinite critical points

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