Complex mixed-mode oscillations based on a modified Rayleigh-Duffing oscillator driven by low-frequency excitations

Chun Zhang, Xindong Ma and Qinsheng Bi

Chaos, Solitons & Fractals, 2022, vol. 160, issue C

Abstract: The complex mixed-mode oscillation patterns are proposed and analyzed in a modified Rayleigh-Duffing oscillator based on the bifurcation theory in this paper. Four mixed-mode oscillations, namely “Homoclinic/Homoclinic-Homoclinic/Homoclinic” intermittent type, “fold/Homoclinic-Homoclinic/supHopf” intermittent type, “fold/Homoclinic-supHopf/supHopf” intermittent type and “fold/Homoclinic” type, are discussed in detail. Considering the low frequency excitations as slow-changing state variables, a modified autonomous system is obtained. The bifurcation characteristics of the fast subsystem are presented briefly by using the bifurcation theory. Then, we investigate the generation principle of the bifurcation delay phenomenon that performs a critical role in the production of two mixed-mode oscillations. This paper presents a fact that the dynamical behaviors are sensitive to the values of the system parameters and the parameters determine different forms of the repetitive spiking states that leads to different patterns of the mixed-mode oscillations. In addition, the theoretical analysis and numerical simulations are compared to illustrate the correctness of this paper.

Keywords: Mixed-mode oscillations; Low frequency excitations; Bifurcation; Hopf bifurcation delay; Slow-fast analysis (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922003940
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922003940

DOI: 10.1016/j.chaos.2022.112184

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().