中国物理B ›› 2007, Vol. 16 ›› Issue (8): 2285-2290.doi: 10.1088/1009-1963/16/8/021

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Nonchaotic random behaviour in the second order autonomous system

徐霞1, 张建峡2, 徐云3, 周红3   

  1. (1)Public-Course Department, Guangdong Police Officer College, Guangzhou 510232, China; (2)School of Electrical Engineering, Guizhou University, Guiyang 550003, China; (3)State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
  • 收稿日期:2006-05-27 修回日期:2007-03-06 出版日期:2007-08-20 发布日期:2007-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 59577025) and the Fundamental Research Foundation of Tsinghua University (Grant No JC2001021).

Nonchaotic random behaviour in the second order autonomous system

Xu Yun(徐云)a)†, Zhang Jian-Xia(张建峡)b), Xu Xia(徐霞)c), and Zhou Hong(周红)a)   

  1. a State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China; b School of Electrical Engineering, Guizhou University, Guiyang 550003, China; c Public-Course Department, Guangdong Police Officer College, Guangzhou 510232, China
  • Received:2006-05-27 Revised:2007-03-06 Online:2007-08-20 Published:2007-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 59577025) and the Fundamental Research Foundation of Tsinghua University (Grant No JC2001021).

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摘要： Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.

关键词: chaos, nonchaotic, random, autonomous system

Abstract: Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.

Key words: chaos, nonchaotic, random, autonomous system

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
02.50.Cw (Probability theory) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)