Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Chaos: An Interdisciplinary Journal of Nonlinear Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.