https://doi.org/10.1140/epjp/s13360-024-05178-z
Regular Article
Bursting dynamic analysis of generalized Duffing systems under two periodic excitations
School of Mathematical Sciences, Zhejiang Normal University, 321004, Jinhua, China
Received:
23
February
2024
Accepted:
14
April
2024
Published online:
29
April
2024
For a class of generalized Duffing systems with two periodic excitations, the complex dynamical behaviors of the systems are investigated. In the first place, the bifurcation conditions and stability of the generalized Duffing system under single-period excitation are analyzed, and the bursting oscillations occurring under typical parameter conditions and their generation mechanisms are given. Then, the fast–slow analysis is applied for numerically simulating the system through time course diagrams and bifurcation diagrams, and the new bursting oscillation modes of the system with different parameters when the ratio of the frequencies of the two excitations is an integer multiple are studied, and the effects of single-excitation amplitude variations as well as double-excitation amplitude variations on the bursting oscillations are further investigated. Finally, by discretizing the system, the transition mechanism of single periodic attractor and chaotic attractor to various attractors are obtained.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
