Chin. Phys. Lett.  2009, Vol. 26 Issue (6): 060506    DOI: 10.1088/0256-307X/26/6/060506
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
Download: PDF(386KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
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
PACS:  05.45.Ac (Low-dimensional chaos)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/26/6/060506       OR      https://cpl.iphy.ac.cn/Y2009/V26/I6/060506
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
YANG Zheng-Ling
GAO Yang
GAO Yong-Tao
ZHANG Jun
[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)
Related articles from Frontiers Journals
[1] Paulo C. Rech. Dynamics in the Parameter Space of a Neuron Model[J]. Chin. Phys. Lett., 2012, 29(6): 060506
[2] LI Xian-Feng**, Andrew Y. -T. Leung, CHU Yan-Dong. Symmetry and Period-Adding Windows in a Modified Optical Injection Semiconductor Laser Model[J]. Chin. Phys. Lett., 2012, 29(1): 060506
[3] JI Ying**, BI Qin-Sheng . SubHopf/Fold-Cycle Bursting in the Hindmarsh–Rose Neuronal Model with Periodic Stimulation[J]. Chin. Phys. Lett., 2011, 28(9): 060506
[4] WANG Xing-Yuan**, QIN Xue, XIE Yi-Xin . Pseudo-Random Sequences Generated by a Class of One-Dimensional Smooth Map[J]. Chin. Phys. Lett., 2011, 28(8): 060506
[5] CAO Qing-Jie, **, HAN Ning, TIAN Rui-Lan . A Rotating Pendulum Linked by an Oblique Spring[J]. Chin. Phys. Lett., 2011, 28(6): 060506
[6] YANG Yang, WANG Cang-Long, DUAN Wen-Shan**, CHEN Jian-Min . Resonance and Rectification in a Two-Dimensional Frenkel–Kontorova Model with Triangular Symmetry[J]. Chin. Phys. Lett., 2011, 28(3): 060506
[7] WEI Du-Qu**, LUO Xiao-Shu, CHEN Hong-Bin, ZHANG Bo . Random Long-Range Interaction Induced Synchronization in Coupled Networks of Inertial Ratchets[J]. Chin. Phys. Lett., 2011, 28(11): 060506
[8] Eduardo L. Brugnago**, Paulo C. Rech. Chaos Suppression in a Sine Square Map through Nonlinear Coupling[J]. Chin. Phys. Lett., 2011, 28(11): 060506
[9] Gabriela A. Casas**, Paulo C. Rech*** . Numerical Study of a Three-Dimensional Hénon Map[J]. Chin. Phys. Lett., 2011, 28(1): 060506
[10] XU Jie, LONG Ke-Ping, FOURNIER-PRUNARET Danièle, TAHA Abdel-Kaddous, CHARGE Pascal. Chaotic Dynamics in a Sine Square Map: High-Dimensional Case (N≥3)[J]. Chin. Phys. Lett., 2010, 27(8): 060506
[11] BAO Bo-Cheng, XU Jian-Ping, LIU Zhong. Initial State Dependent Dynamical Behaviors in a Memristor Based Chaotic Circuit[J]. Chin. Phys. Lett., 2010, 27(7): 060506
[12] JI Ying, BI Qin-Sheng. Spiking Behavior in Chua's Circuit[J]. Chin. Phys. Lett., 2010, 27(6): 060506
[13] LI Fei, PAN Chang-Ning, ZHANG Dong-Xia, TANG Li-Qiang. Chaotic Dynamics of a Josephson Junction with Nonlinear Damping[J]. Chin. Phys. Lett., 2010, 27(5): 060506
[14] ZHANG Gang, ZHANG Wei, LIU Zeng-Rong. Synchronization of Coupled Nonidentical Dynamical Systems[J]. Chin. Phys. Lett., 2010, 27(3): 060506
[15] DONG Gao-Gao, ZHENG Song, TIAN Li-Xin, DU Rui-Jin,. Spectrum Analysis and Circuit Implementation of a New 3D Chaotic System with Novel Chaotic Attractors[J]. Chin. Phys. Lett., 2010, 27(2): 060506
Viewed
Full text


Abstract