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Bursting dynamic analysis of generalized Duffing systems under two periodic excitations

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Abstract

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 data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through grant No.12172333 and the Natural Science Foundation of Zhejiang through grant No.LY20A020003.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China

    Youhua Qian, Danjin Zhang & Mengmeng Leng

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  1. Youhua Qian
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  2. Danjin Zhang
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  3. Mengmeng Leng
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Correspondence to Youhua Qian.

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Qian, Y., Zhang, D. & Leng, M. Bursting dynamic analysis of generalized Duffing systems under two periodic excitations. Eur. Phys. J. Plus 139, 366 (2024). https://doi.org/10.1140/epjp/s13360-024-05178-z

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