Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation
Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation
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DOI：
10.1007/s40314-013-0105-8
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发表时间：
2013-11
影响因子：
2.6
通讯作者：
E. Kutafina
中科院分区：
文献类型：
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作者：
E. Kutafina
在Shimizu等人的论文（Phys Lett A 375：1566，2011）之后，我们考虑具有非自治周期扰动的Bonhoven-van der Pol振荡器。我们表明，该文件中报道的混合模式振荡的存在下，可以使用几何奇异摄动理论解释。所考虑的模型可以重写为一个四维（局部三维）自治系统，在一定条件下，有一个折叠的鞍结奇点，另外可以被视为一个三时间尺度之一。
Following the paper of Shimizu et al. (Phys Lett A 375:1566, 2011), we consider the Bonhoeffer-van der Pol oscillator with non-autonomous periodic perturbation. We show that the presence of mixed mode oscillations reported in that paper can be explained using the geometric singular perturbation theory. The considered model can be re-written as a four-dimensional (locally three-dimensional) autonomous system, which under certain conditions has a folded saddle-node singularity and additionally can be treated as a three time scale one.