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Disappearance and reappearance of chaos

Author

Listed:
  • Bin Zhang

    (Computer College, Weinan Normal University, Weinan 714099, P. R. China†School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119 P. R. China)

  • Sheng-Jun Wang

    (#x2020;School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119 P. R. China)

  • Shi-Xian Qu

    (#x2020;School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119 P. R. China)

Abstract

The disappearance and reappearance of chaos by adjusting the internal parameters of dynamics in Lorenz system are studied. We observe monotonous and periodic time-dependent changes of Rayleigh number. There exists relaxation time for the disappearance of chaos, when we use the snapshot attractors to observe the change of the system attractors. We show that the rate of disappearance and reappearance of chaos is positively correlated with the control parameters. To reflect the relaxation phenomenon of chaotic disappearance and the sensitivity of trajectory, the concept of finite-time Lyapunov exponent is used. Then the statistical characteristics of the system can be presented by standard deviation. The chaotic disappearance and reappearance are manifested in the decrease and increase of the standard deviation. The standard deviation decreases continuously during chaotic disappearance, but increases discontinuously during chaotic reappearance. A distinctive scenario is that no matter which parameter changes, when we use the same rate of change in the process of chaotic disappearance and reappearance, their paths are different.

Suggested Citation

  • Bin Zhang & Sheng-Jun Wang & Shi-Xian Qu, 2021. "Disappearance and reappearance of chaos," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(09), pages 1-16, September.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:09:n:s0129183121501254
    DOI: 10.1142/S0129183121501254
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