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Countless coexisting chaotic attractors: From system construction to FPGA-based observation

Author

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  • Pan, Guohao
  • Li, Chunbiao
  • Liu, Wangyu
  • Xue, Yishi
  • Qi, Xiaolong

Abstract

Coexisting chaotic attractors provide much more convenience for the diverse outputs of chaos. At the same time, multistable chaotic systems exhibit strong uncertainty and complexity. Therefore, the chaotic system with multistable states plays an important role in specific application situations. In this paper, a chaotic system is transformed to be the one outputting countless coexisting chaotic attractors by expanding the dimension of the system or embedding the function of the feedback. The introduction of complex feedback contributes to the generation of chaos, while the embedding of fixed functions facilitates the constraints on the offset within the system variables. In this framework, adjusting the linear function constraint relationship between offset-interlocked variables can also regulate the distribution direction of coexisting attractors. The work shows the simple candidates with offset constraints outputting countless coexisting attractors, where some of the system variables with different average values can be triggered through the initial conditions. Based on FPGA, all the phenomenon associated with the coexisting attractors are observed by the initial condition selection.

Suggested Citation

  • Pan, Guohao & Li, Chunbiao & Liu, Wangyu & Xue, Yishi & Qi, Xiaolong, 2025. "Countless coexisting chaotic attractors: From system construction to FPGA-based observation," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s096007792500623x
    DOI: 10.1016/j.chaos.2025.116610
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