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Volume 7 Issue 4
Jun.  2020

IEEE/CAA Journal of Automatica Sinica

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Xiaoyuan Wang, Chenxi Jin, Xiaotao Min, Dongsheng Yu and Herbert Ho Ching Iu, "An Exponential Chaotic Oscillator Design and Its Dynamic Analysis," IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1081-1086, July 2020. doi: 10.1109/JAS.2020.1003252
Citation: Xiaoyuan Wang, Chenxi Jin, Xiaotao Min, Dongsheng Yu and Herbert Ho Ching Iu, "An Exponential Chaotic Oscillator Design and Its Dynamic Analysis," IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1081-1086, July 2020. doi: 10.1109/JAS.2020.1003252

An Exponential Chaotic Oscillator Design and Its Dynamic Analysis

doi: 10.1109/JAS.2020.1003252
Funds:  This work was supported by the National Natural Science Foundation of China (61871429), and the Natural Science Foundation of Zhejiang Province (LY18F010012)
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  • After years of development, chaotic circuits have possessed many different mathematic forms and multiple realization methods. However, in most of the existing chaotic systems, the nonlinear units are composed of the product terms. In this paper, in order to obtain a chaotic oscillator with higher nonlinearity and complexity to meet the needs of utilization, we discuss a novel chaotic system whose nonlinear term is realized by an exponential term. The new exponential chaotic oscillator is constructed by adding an exponential term to the classical Lü system. To further investigate the dynamic characteristics of the oscillator, classical theoretical analyses have been performed, such as phase diagrams, equilibrium points, stabilities of the system, Poincaré mappings, Lyapunov exponent spectrums, and bifurcation diagrams. Then through the National Institute of Standards and Technology (NIST) statistical test, it is proved that the chaotic sequence generated by the exponential chaotic oscillator is more random than that produced by the Lü system. In order to further verify the practicability of this chaotic oscillator, by applying the improved modular design method, the system equivalent circuit has been realized and proved by the Multisim simulation. The theoretical analysis and the Multisim simulation results are in good agreement.

     

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    Highlights

    • Exponential nonlinear term
      The exponential term in this system makes it different from the original chaotic system. This exponentially nonlinear term may make the new chaotic system have better performance. And the effectiveness of this exponential chaotic system has been proved by various theoretical analyses.
    • NIST test
      The exponential chaotic system passed all fifteen tests, but the Lü system passed only fourteen of them. Also the exponential chaotic system has 9 tests with P-values greater than the Lü system in all 15 tests. It shows that the sequence generated by the exponential chaotic system is more random than that produced by the Lü system.
    • Circuit
      This paper has designed a circuit corresponding to the exponential chaotic system. And the simulation results of Multisim are consistent with the theoretical analysis. This proves the effectiveness of the chaotic circuit. The circuit allows the chaotic system to be further applied to future applications.

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