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Coexistence and ergodicity in a variant Nosé-Hoover oscillator and its FPGA implementation

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Abstract

As a classical volume-conservative system, the Nosé-Hoover oscillator can generate conservative chaos and nested invariant tori. In this paper, a new 3D system is derived from the Nosé-Hoover oscillator in which the coexisting phenomenon of conservative flow and dissipative attractor is discovered. We first numerically analyze the equilibrium points and their stabilities, and study the fold-Hopf bifurcation at the critical point. Then, the dynamic behaviors of the system are studied, besides the coexisting phenomenon, the system also has transient chaos. More interestingly, we find that the increase of parameter has a significant effect on enhancing the ergodicity of the system, which is also proved by the cross section with no “holes”. Furthermore, we design a pseudo-random number generator based on the new system. Numerical results show that this PRNG can generate pseudo-random sequences with high randomness and is suitable for image encryption. Finally, we implement the system using FPGA technology.

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Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 61973175 and 61903274), the TianJin Natural Science Foundation (Grant Nos. 20JCYBJC01060 and 20JCQNJC01450), and the Tianjin Research Innovation Project for Postgraduate Students (Grant No.2021YJSB034).

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Authors and Affiliations

  1. College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

    Yue Li

  2. Department of Earth and Space Science and Engineering, York University, 4700 Keele St, Toronto, M3J 1P3, Canada

    Mingfeng Yuan

  3. College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin, 300222, China

    Zhonggao Chen

  4. College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

    Zengqiang Chen

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  1. Yue Li
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Correspondence to Yue Li.

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Li, Y., Yuan, M., Chen, Z. et al. Coexistence and ergodicity in a variant Nosé-Hoover oscillator and its FPGA implementation. Nonlinear Dyn 111, 10583–10599 (2023). https://doi.org/10.1007/s11071-023-08347-4

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