GENERAL |
|
|
|
|
Behavior of a Logistic Map Driven by White Noise |
YANG Zheng-Ling, GAO Yang, GAO Yong-Tao, ZHANG Jun |
1School of Electrical Engineering and Automation, Tianjin University, Tianjin 3000722Tianjin Key Laboratory of Process Measurement and Control, Tianjin 300072 |
|
Cite this article: |
YANG Zheng-Ling, GAO Yang, GAO Yong-Tao et al 2009 Chin. Phys. Lett. 26 060506 |
|
|
Abstract In the real world, every nonlinear system is inevitably affected by noise. As an example, a logistic map driven by white noise is studied. Unlike previous studies which focused on the behavior under local parameters to find analytical results, we investigate the whole driven logistic map. For a white noise driven logistic map, its non-divergent interval decreases with increasing white noise. The white noise does not change the equilibrium point and two-cycle intervals in statistics, if the driven logistic map is kept non-divergent. In particular, chaos can be excited by white noise only after the four-cycle bifurcation begins. The latest result is a necessary condition which has not been given in the literature [Int. J. Bifur. Chaos 18(2008)509], and it can be deduced from Sharkovsky's theorem. Numerical simulations prove these analytical results.
|
Keywords:
05.45.Ac
|
|
Received: 08 November 2009
Published: 01 June 2009
|
|
|
|
|
|
[1] Hao B L 1993 Starting with Parabolas: An Introductionto Chaotic Dynamics (Shanghai: Shanghai Scientific andTechnological Education Publishing House) (in Chinese) [2] Chen S G 1992 Mapping and Chaos (Beijing: NationalDefence Industry Press) (in Chinese) [3] Shi P L 2008 Chaos 18 013122 [4] Negi S S et al 2000 Physica D 145 1 [5] Li F G 2008 Central Eur. J. Phys. 6 539 [6] Baldovin F and Robledo1 A 2005 Phys. Rev. E 72 066213 [7] Fogedby H C et al 2005 J. Statist. Phys. 121759 [8] Erguler K et al 2008 Mathem. Biosci. 216 90 [9] Shi P L et al 2001 Phys. Rev. E 63 046310 [10] Shi P L et al 2001 Commun. Theor. Phys. 35389 [11] Shuai J W et al 2000 Phys. Lett. A 267 335 [12] Elhadj Z and Sprott J C 2008 Chaos 18 023119 [13] Wang X Y et al 2008 Acta Phys. Sin. 57 736(in Chinese) [14] Gan J C et al 2003 Acta Phys. Sin. 52 1085(in Chinese) [15] Yu J J et al 2006 Acta Phys. Sin. 55 0042 (inChinese) [16] Almeida J et al 2005 Physica D 200 124 [17] Yang Z L et al 2007 Chin. Phys. Lett. 24 1170 [18] Li X C, Xu W and Li R H 2008 Chin. Phys. B 17 557 [19] Tel T et al 2008 Int. J. Bifur. Chaos 18 509 [20] Horn R A and Johnson C R 2005 Matrix analysis(Beijing: Posts {\& Telecom Press) |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|