Using the averaging theory of second order, we study the limit cycles which bifurcate from a zero-Hopf equilibrium point of polynomial vector fields with cubic nonlinearities in \(\mathbb {R}^{n}\). We prove that there are at least 3^n− 2 limit cycles bifurcating from such zero-Hopf equilibrium points. Moreover, we provide an example in dimension 6 showing that this number of limit cycles is reached.

中文翻译：

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基于二阶平均理论的多项式微分系统的N维零霍夫分支

使用二阶平均理论，我们研究了在\（\ mathbb {R} ^ {n} \）中具有三次非线性的多项式矢量场的零-霍夫夫平衡点分叉的极限环。我们证明了从这样的零霍夫平衡点分叉出至少3 ^{n -2个}极限环。此外，我们在维度6中提供了一个示例，显示达到了此极限循环数。