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Acta Mechanica Sinica
Erschienen in: Acta Mechanica Sinica 4/2020

08.07.2020 | Research Paper

Cluster oscillation and bifurcation of fractional-order Duffing system with two time scales

verfasst von: Yanli Wang, Xianghong Li, Yongjun Shen

Erschienen in: Acta Mechanica Sinica | Ausgabe 4/2020

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Abstract

The dynamical behavior on fractional-order Duffing system with two time scales is investigated, and the point-cycle coupling type cluster oscillation is firstly observed herein. When taking the fractional order as bifurcation parameter, the dynamics of the autonomous Duffing system will become more complex than the corresponding integer-order one, and some typical phenomenon exist only in the fractional-order one. Different attractors exist in various parameter space, and Hopf bifurcation only happens while fractional order is bigger than 1 under certain parameter condition. Moreover, the bifurcation behavior of the autonomous system may regulate dynamical phenomenon of the periodic excited system. It results into the point-cycle coupling type cluster oscillation when the fractional order is bigger than 1. The related generation mechanism based on slow-fast analysis method is that the slow variation of periodic excitation makes the system periodically visit different attractors and critical points of different bifurcations of the autonomous system.

Graphic abstract

Vorheriger Artikel Harmonic balance-based approach for optimal time delay to control unstable periodic orbits of chaotic systems
Nächster Artikel Forced vibration of smart laminated viscoelastic plates by RPT finite element approach

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Metadaten
Titel
Cluster oscillation and bifurcation of fractional-order Duffing system with two time scales
verfasst von
Yanli Wang
Xianghong Li
Yongjun Shen
Publikationsdatum
08.07.2020
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 4/2020
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-020-00967-y

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