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N -Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order
Journal of Dynamical and Control Systems ( IF 0.6 ) Pub Date : 2020-06-29 , DOI: 10.1007/s10883-020-09501-6
S. Kassa , J. Llibre , A. Makhlouf

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 3n− 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:

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。

更新日期:2020-06-29
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