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)
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
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.
Received: 27 May 2006
Revised: 06 March 2007
Accepted manuscript online:
(Fluctuation phenomena, random processes, noise, and Brownian motion)
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 59577025) and the
Fundamental Research Foundation of Tsinghua University (Grant No
JC2001021).
Cite this article:
Xu Yun(徐云), Zhang Jian-Xia(张建峡), Xu Xia(徐霞), and Zhou Hong(周红) Nonchaotic random behaviour in the second order autonomous system 2007 Chinese Physics 16 2285
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