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Codimension-two three-grazing bifurcations of a conveyor belt system with rigid and elastic constraints

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  • Shi, Bairu
  • Li, Qunhong
  • Zhang, Wei

Abstract

The friction-collision system is a key focus in the study of non-smooth dynamics due to its complexity and importance. High-codimension bifurcations in friction-collision systems are a difficult research problem in this field because of the lack of mathematical tools. Currently, no effective method has been found in the literature to analyze the codimension-two bifurcation caused by the combined effects of collision and friction in friction-collision systems. However, studying codimension-two bifurcation in friction-collision systems is crucial for understanding the system's dynamic behavior. To explore this issue, this paper examines a single-degree-of-freedom conveyor belt system featuring asymmetric rigid-elastic hybrid constraints as an example for theoretical and numerical research. The zero-time discontinuity mapping and the smooth Poincaré mapping are combined to obtain the global Poincaré mapping of three-grazing periodic motion. This global compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. Numerical simulations are conducted based on these theoretical results. The codimension-two three-grazing bifurcation points are located in the friction-collision system, confirming the accuracy of the method and first discovering the overlapping phenomenon of these points. Two-parameter bifurcation diagrams near codimension-two three-grazing bifurcation points are drawn, where very rich dynamic phenomena such as typical sliding bifurcations, flutter, and periodic cascades are observed. In particular, some new bifurcation curves unique to the friction-collision system are discovered.

Suggested Citation

  • Shi, Bairu & Li, Qunhong & Zhang, Wei, 2026. "Codimension-two three-grazing bifurcations of a conveyor belt system with rigid and elastic constraints," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015310
    DOI: 10.1016/j.chaos.2025.117518
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    References listed on IDEAS

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    1. Zheng, Yanxiao & Li, Qunhong & Zhang, Wei & Lei, Jinfeng, 2023. "Three-dimensional mapping analysis of a capsule system with bilateral elastic constraints," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Qunhong Li & Limei Wei & Jieyan Tan & Jiezhen Xi, 2014. "Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, June.
    3. Hany A. Hosham & Mashael A. Aljohani & Eman D. Abou Elela & Nada A. Almuallem & Thoraya N. Alharthi, 2024. "Hidden-like Attractors in a Class of Discontinuous Dynamical Systems," Mathematics, MDPI, vol. 12(23), pages 1-14, November.
    4. Qunhong Li & Limei Wei & Jieyan Tan & Jiezhen Xi, 2014. "Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Peng, Ruyue & Li, Qunhong & Zhang, Wei, 2024. "Homoclinic bifurcation analysis of a class of conveyor belt systems with dry friction and impact," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    6. Watanabe, Masahisa & Prasad, Awadhesh & Sakai, Kenshi, 2024. "Delayed feedback active suspension control for chaos in quarter car model with jumping nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
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