Wei Zhouchao, Kumarasamy Suresh, Ramasamy Mohanasubha, Rajagopal Karthikeyan, Qian Youhua
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China.
Chaos. 2023 Sep 1;33(9). doi: 10.1063/5.0158100.
In the present study, we investigate the dynamic behavior of the fractional-order Bonhoeffer-van der Pol (BVP) oscillator. Previous studies on the integer-order BVP have shown that it exhibits mixed-mode oscillations (MMOs) with respect to the frequency of external forcing. We explore the effect of fractional-order on these MMOs and observe interesting phenomena. For fractional-order q1, we find that as we vary the frequency of external forcing, the system exhibits increasingly small amplitude oscillations. Eventually, as q1 decreases, the MMOs disappear entirely, indicating that lower fractional orders eliminate the presence of MMOs in the BVP oscillator. On the other hand, for the fractional-order q2, we observe more complex MMOs compared to q1. However, we find that the elimination of MMOs occurs with less variation from the integer order 1. Intriguingly, as we change q2, the fractional-order BVP oscillator undergoes a phenomenon known as a crisis, where the attractor expands and extreme events occur. Overall, our study highlights the rich dynamics of the fractional-order BVP oscillator and its ability to display various modes of oscillations and crises as the order is changed.
在本研究中，我们研究了分数阶邦霍夫尔-范德波尔（BVP）振荡器的动态行为。先前关于整数阶BVP的研究表明，它在外部强迫频率方面表现出混合模式振荡（MMO）。我们探讨了分数阶对这些MMO的影响，并观察到有趣的现象。对于分数阶q1，我们发现随着外部强迫频率的变化，系统表现出振幅越来越小的振荡。最终，随着q1减小，MMO完全消失，这表明较低的分数阶消除了BVP振荡器中MMO的存在。另一方面，对于分数阶q2，与q1相比，我们观察到更复杂的MMO。然而，我们发现MMO的消除在与整数阶1的变化较小的情况下发生。有趣的是，当我们改变q2时，分数阶BVP振荡器会经历一种称为危机的现象，即吸引子扩展并发生极端事件。总体而言，我们的研究突出了分数阶BVP振荡器丰富的动力学特性及其在阶数变化时展示各种振荡模式和危机的能力。
