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Transient dynamics in a quasiperiodically forced nonsmooth dynamical system

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Abstract

Transient chaos is very common in periodically forced dynamical systems, but transient strange nonchaotic dynamics have not been studied by researchers. Therefore, it is meaningful to explore the dynamical phenomena of transient chaos and transient strange nonchaos. In this paper, we investigate a quasiperiodically forced cantilever beam system with impacts and discover abundant transient dynamic phenomena. Firstly, we determine the transient interval by the bifurcation diagram and the maximum Lyapunov exponent and investigate the correspondence between them. Secondly, we identify transient chaos and transient strange nonchaos and distinguish transient attractors and permanent attractors using the maximum Lyapunov exponent. Furthermore, we verify the strange property of attractors through the phase sensitivity and the power spectrum.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We sincerely thank the people who give valuable comments. The paper is supported by the National Natural Science Foundation of China (Nos. 11832009, 12072291, 12362002, and 12172306).

Funding

The paper is supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2023203019), and the National Natural Science Foundation of China (Nos. 12362002, and 12172306).

Author information

Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, 066004, China

    Gaolei Li, Chen Wang & Shuning Deng

  2. Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao, 066004, China

    Gaolei Li

  3. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Jicheng Duan

  4. School of Mathematics and Statistics, Hexi University, Zhangye, 734000, China

    Denghui Li

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  1. Gaolei Li
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  2. Jicheng Duan
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Contributions

Gaolei Li helped in methodology, formal analysis, writing—original draft. Jicheng Duan contributed to formal analysis, writing—review & editing. Denghui Li and Shuning Deng validated the study. Chen Wang was involved in methodology.

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Correspondence to Jicheng Duan.

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Li, G., Duan, J., Li, D. et al. Transient dynamics in a quasiperiodically forced nonsmooth dynamical system. Nonlinear Dyn 112, 6205–6214 (2024). https://doi.org/10.1007/s11071-024-09370-9

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