Period-doubling route to mixed-mode chaos
Period-doubling route to mixed-mode chaos
复制标题
通向混合模式混沌的倍周期路线
DOI：
10.1103/physreve.104.024211
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发表时间：
2021
影响因子：
2.4
通讯作者：
Epstein, Irving R.
中科院分区：
文献类型：
--
作者：
Awal, Naziru M.;Epstein, Irving R.
混合模式振荡（MMO）是一种复杂的动力学行为，其中每个振荡周期由一个或多个大振幅尖峰以及随后的一个或多个小振幅峰值组成。MMO通常在参数变化下经历加周期分叉。在这里，我们证明了，在一组三个相同的，线性耦合的货车德尔波尔振荡器，一个场景中，MMO表现出一个周期加倍序列混沌，保持MMO结构，以及周期添加分叉。我们的特点的MMO的混沌性质，并归因于它们的存在，以一个主-从式强迫的内部振荡器的外部两个有足够的相位差。一个单一的非自治振荡器被迫由两个正弦函数的模拟支持这种解释，并建议MMO倍周期的情况可能更普遍。
Mixed-mode oscillations (MMOs) are a complex dynamical behavior in which each cycle of oscillation consists of one or more large amplitude spikes followed by one or more small amplitude peaks. MMOs typically undergo period-adding bifurcations under parameter variation. We demonstrate here, in a set of three identical, linearly coupled van der Pol oscillators, a scenario in which MMOs exhibit a period-doubling sequence to chaos that preserves the MMO structure, as well as period-adding bifurcations. We characterize the chaotic nature of the MMOs and attribute their existence to a master-slave-like forcing of the inner oscillator by the outer two with a sufficient phase difference between them. Simulations of a single nonautonomous oscillator forced by two sine functions support this interpretation and suggest that the MMO period-doubling scenario may be more general.