Noise destroys the coexisting of periodic orbits of a piecewise linear map

doi:10.1088/1674-1056/22/3/030502

中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/22/3/030502

Noise destroys the coexisting of periodic orbits of a piecewise linear map

王参军^{a b}, 杨科利^{a b}, 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

收稿日期:2012-07-19 修回日期:2012-09-10 出版日期:2013-02-01 发布日期:2013-02-01
基金资助:
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).

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

Received:2012-07-19 Revised:2012-09-10 Online:2013-02-01 Published:2013-02-01
Contact: Qu Shi-Xian E-mail:sxqu@snnu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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 τ_c<τ<τ_c', only the orbits of P-5 appear, and the stability of the orbits of P-5 is enhanced. However, when τ>τ_c' (τ_c and τ_c' are critical values), only the orbits of P-6 exist, and the stability of the orbits of P-6 is enhanced greatly. When τ<τ_c, 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.

关键词: piecewise linear map, noise, periodic orbit

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 τ_c<τ<τ_c', only the orbits of P-5 appear, and the stability of the orbits of P-5 is enhanced. However, when τ>τ_c' (τ_c and τ_c' are critical values), only the orbits of P-6 exist, and the stability of the orbits of P-6 is enhanced greatly. When τ<τ_c, 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.

Key words: piecewise linear map, noise, periodic orbit

中图分类号: (Noise)

05.40.Ca

05.45.Ac (Low-dimensional chaos)

王参军, 杨科利, 屈世显. Noise destroys the coexisting of periodic orbits of a piecewise linear map[J]. 中国物理B, 2013, 22(3): 30502-030502.

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[J]. Chin. Phys. B, 2013, 22(3): 30502-030502.

参考文献 32

[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

Noise destroys the coexisting of periodic orbits of a piecewise linear map

Noise destroys the coexisting of periodic orbits of a piecewise linear map

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