|
|
Noise destroys the coexisting of periodic orbits of a piecewise linear map |
Wang Can-Jun (王参军)a b, Yang Ke-Li (杨科利)a b, Qu Shi-Xian (屈世显)a |
a Institute of Theoretical & Computational Physics, School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China; b Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China |
|
|
Abstract The effects of the Gaussian white noise and the Gaussian colored noise on the periodic orbits of period-5 (P-5) and period-6 (P-6) in their coexisting domain of a piecewise linear map are investigated numerically. The probability densities of some orbits are calculated. When the noise intensity is D=0.0001, only the orbits of P-5 exist, and the coexisting phenomenon is destroyed. On the other hand, the self-correlation time τ of the colored noise also affects the coexisting phenomenon. When τc<τ<τc', only the orbits of P-5 appear, and the stability of the orbits of P-5 is enhanced. However, when τ>τc' (τc and τc' are critical values), only the orbits of P-6 exist, and the stability of the orbits of P-6 is enhanced greatly. When τ<τc, the orbits of P-5 and P-6 coexist, but the stability of the orbits of P-5 is enhanced and that of P-6 is weakened with τ increasing.
|
Received: 19 July 2012
Revised: 10 September 2012
Accepted manuscript online:
|
PACS:
|
05.40.Ca
|
(Noise)
|
|
05.45.Ac
|
(Low-dimensional chaos)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10875076), the Science Foundation of the Education Bureau of Shaanxi Province, China (Grant No. 12JK0962), and the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK11053). |
Corresponding Authors:
Qu Shi-Xian
E-mail: sxqu@snnu.edu.cn
|
Cite this article:
Wang Can-Jun (王参军), Yang Ke-Li (杨科利), Qu Shi-Xian (屈世显) Noise destroys the coexisting of periodic orbits of a piecewise linear map 2013 Chin. Phys. B 22 030502
|
[1] |
Wu D J, Cao L and Ke S Z 1994 Phys. Rev. E 50 2496
|
[2] |
Cao L, Wu D J and Ke S Z 1995 Phys. Rev. E 52 3228
|
[3] |
Mantegna R N and Spagnolo B 1996 Phys. Rev. Lett. 76 563
|
[4] |
Mielke A 2000 Phys. Rev. Lett. 84 818
|
[5] |
Ai B Q, Wang X J, Liu G T and Liu L G 2003 Phys. Rev. E 67 022903
|
[6] |
Mei D C, Xie C W and Zhang L 2004 Eur. Phys. J. B 41 107
|
[7] |
Wang C J, Wei Q and Mei D C 2008 Phys. Lett. A 372 2176
|
[8] |
Wang C J, Wei Q and Zheng B B 2008 Acta Phys. Sin. 57 1375 (in Chinese)
|
[9] |
Jiang L L, Luo X Q, Wu D and Zhu S Q 2012 Chin. Phys. B 21 090503
|
[10] |
Liu Q and Jia Y 2004 Phys. Rev. E 70 041907
|
[11] |
Jia Z L and Mei D C 2012 Eur. Phys. J. B 85 139
|
[12] |
Yang M, Li X L and Wu D J 2012 Acta Phys. Sin. 61 160502 (in Chinese)
|
[13] |
Zhang L, Yuan X H and Wu L 2012 Acta Phys. Sin. 61 110501 (in Chinese)
|
[14] |
Guo Y F and Tan J G 2012 Acta Phys. Sin. 61 170502 (in Chinese)
|
[15] |
Duan W L, Yang L J and Mei D C 2011 Chin. Phys. B 20 030503
|
[16] |
Crutchfield J P and Huberman B A 1980 Phys. Lett. A 77 407
|
[17] |
Crutchfield J P, Farmer J D and Huberman B A 1982 Phys. Rep. 92 45
|
[18] |
Gao J B, Hwang S K and Liu J M 1999 Phys. Rev. Lett. 82 1132
|
[19] |
Hwang S K, Gao J B and Liu J M 2000 Phys. Rev. E 61 5162
|
[20] |
Serletis A, Shahmoradi A and Serletis D 2007 Chaos Soliton. Fract. 33 914
|
[21] |
Serletis A, Shahmoradi A and Serletis D 2007 Chaos Soliton. Fract. 32 883
|
[22] |
Serletis D 2008 Chaos Soliton. Fract. 38 921
|
[23] |
Li F G 2008 Cent. Eur. J. Phys. 6 539
|
[24] |
Li F G and Ai B Q 2011 Commun. Theor. Phys. 55 1001
|
[25] |
Grudzinski K and Zebrowski J 2004 Physica A 336 153
|
[26] |
He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W and Christiansen B 1994 Physica D 79 335
|
[27] |
Wang J, Ding X L, Hu Bambi Hu, Wang B H, Mao J S and He D R 2001 Phys. Rev. E 64 026202
|
[28] |
Ren H P and Liu D 2005 Chin. Phys. 14 1352
|
[29] |
He D R, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B and Wang B H 1992 Phys. Lett. A 171 61
|
[30] |
Qu S X, Wu S G and He D R 1998 Phys. Rev. E 57 402
|
[31] |
Qu S X, Wu S G and He D R 1997 Phys. Lett. A 231 152
|
[32] |
Qu S X, Lu R Z, Zhang L and He D R 2008 Chin. Phys. B 17 4418
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|