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Behavior similar to period-doubling bifurcation in chaotic and hyperchaotic states

Author

Listed:
  • Zhang, Xili
  • Chen, Xinghui
  • Wang, Qiao
  • Li, Kunshuai
  • Tian, Zean
  • Liuli, Anke
  • Meng, Xiangjie

Abstract

The emergence of discrete memristor theory has rapidly propelled this field to become a focal point in nonlinear system research. In this study, a novel three-dimensional discrete memristive chaotic map (3D hyper-map) is constructed, and the Lyapunov exponent can be effectively controlled by adjusting its internal frequency parameters. It is particularly noteworthy that when this 3D hyper-map system is in a chaotic state, it exhibits quadfurcation or multifurcation behaviors analogous to period-doubling bifurcation. Analysis of its spectral entropy distribution indicates that the system possesses high complexity within the parameter range. Finally, the exhibited offset boosting behavior is elaborated. This 3D hyper-map has been implemented on the STM32 platform and further applied to the design of a pseudo-random number generator, whose high randomness has been validated through the NIST SP800–22 statistical test suite.

Suggested Citation

  • Zhang, Xili & Chen, Xinghui & Wang, Qiao & Li, Kunshuai & Tian, Zean & Liuli, Anke & Meng, Xiangjie, 2025. "Behavior similar to period-doubling bifurcation in chaotic and hyperchaotic states," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p3:s0960077925011658
    DOI: 10.1016/j.chaos.2025.117152
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    References listed on IDEAS

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