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A simplest Lorenz-like chaotic circuit and its applications in secure communication and weak signal detection

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Abstract

This paper is devoted to introduce a simplest Lorenz-like chaotic circuit and the calculation of Hamiltonian energy function for the corresponding dimensionless Lorenz-like chaotic system, as well as its applications in weak signal detection and chaotic secure communication. First, a simplest Lorenz-like chaotic circuit composed of three operational amplifiers and two analog multipliers is constructed through simplified circuit design based on a Lorenz chaotic circuit composed of six operational amplifiers and two analog multipliers. Then, the weak signal detection problem of the corresponding Lorenz-like chaotic system is studied by utilizing the extreme sensitivity of chaotic system to initial value in consideration of the inaccuracy of traditional detection methods. Furthermore, the Hamiltonian energy function of the Lorenz-like chaotic system is calculated based on the Helmholtz theorem. In addition, the simplest Lorenz-like chaotic circuit is applied to construct a chaotic secure communication system using the active control synchronization method. Accordingly, the hardware circuits are implemented to prove the effectiveness and feasibility of the simplest Lorenz-like chaotic circuit and the chaotic secure communication circuit.

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Funding

The authors are greatly thankful for the help and support from the National Natural Science Foundation of China (Grant No. 62061014), the Innovation fund project of colleges and universities in Gansu Province in 2020 (Grant No. 2020B-204), and the Key Projects of President fund for scientific research innovation and application of Hexi University (Grant No. XZZD2019005).

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Authors and Affiliations

  1. School of Physics and Electromechanical Engineering, Hexi University, Zhangye, 734000, China

    Li Xiong, Liwan Qi & Qishan Wang

  2. Department of Hydraulics, Changjiang River Scientific Research Institute, Wuhan, 430010, China

    Sufen Teng

  3. College of Electricity and New Energy, China Three Gorges University, Yichang, 443002, China

    Lu Wang

  4. School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, China

    Xinguo Zhang

Authors
  1. Li Xiong
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  2. Liwan Qi
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  3. Sufen Teng
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  4. Qishan Wang
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  5. Lu Wang
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  6. Xinguo Zhang
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Contributions

LX is mainly responsible for circuit design and dynamics analysis of the proposed Lorenz-like chaotic system, as well as the paper writing. LQ is mainly responsible for circuit simulation and hardware implementation of the proposed Lorenz-like chaotic system. ST is mainly responsible for numerical analysis of dynamic characteristics. QW is mainly responsible for hardware realization of the chaotic secure communication circuit. LW is mainly responsible for circuit simulation and English embellishment. XZ is mainly responsible for circuit design.

Corresponding author

Correspondence to Li Xiong.

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The authors have declared that no competing interests exist.

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Xiong, L., Qi, L., Teng, S. et al. A simplest Lorenz-like chaotic circuit and its applications in secure communication and weak signal detection. Eur. Phys. J. Spec. Top. 230, 1933–1944 (2021). https://doi.org/10.1140/epjs/s11734-021-00177-y

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00177-y

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