Stochastic period-doubling bifurcation analysis of a Rössler system with a bounded random parameter

doi:10.1088/1674-1056/19/1/010510

Abstract This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rössler system with an arch-like bounded random parameter. First, we transform the stochastic Rössler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Rössler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rössler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rössler system.

Keywords: Chebyshev polynomial approximation stochastic Rössler system stochastic period-doubling bifurcation bounded random parameter

Received: 26 May 2009
Revised: 20 July 2009
Accepted manuscript online:

PACS:	05.45.Pq	(Numerical simulations of chaotic systems)
	02.10.De	(Algebraic structures and number theory)
	02.30.Mv	(Approximations and expansions)
	02.30.Oz	(Bifurcation theory)
	02.50.Ey	(Stochastic processes)
	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10872165).

Cite this article:

Ni Fei(倪菲), Xu Wei(徐伟), Fang Tong(方同), and Yue Xiao-Le(岳晓乐) Stochastic period-doubling bifurcation analysis of a Rössler system with a bounded random parameter 2010 Chin. Phys. B 19 010510

[1]	Spanos P D and Ghanem R G 1989 J. Eng. Mech. Div. ASCE 115 1035
[2]	Jense H and Iwan W D 1992 J. Eng. Mech. Div. ASCE 118 1012
[3]	Li J 1996 Acta Mech. Sin. 28 63 (in Chinese)
[4]	Fang T, Leng X L and Song C Q 2003 J. Sound. Vib. 226 198
[5]	Fang T, Leng X L, Ma X P and Meng G 2004 Acta Mech. Sin. 20 292 (in Chinese)
[6]	Leng X L, Wu C L, Ma X P, Meng G and Fang T 2005 Nonlinear Dynamics 42 185
[7]	Ma S J, Xu W, Li W and Fang T 2006 Chin. Phys. 15 1231
[8]	Sun X J, Xu W and Ma S J 2006 Acta Phys. Sin. 55 610 (in Chinese)
[9]	Zhang Y, Xu W, Sun X J and Fang T 2007 Acta Phys. Sin. 56 5665 (in Chinese)
[10]	Zhang Y, Xu W and Fang T 2007 Chin. Phys. 16 1923
[11]	Li G J, Xu W, Wang L and Feng J Q 2008 Acta Phys. Sin. 57 2107 (in Chinese)
[12]	Xu W, Ma S J and Xie W X 2008 Chin. Phys. B 17 857
[13]	Ma S J and Xu W 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 2256
[14]	Feng J Q, Wu W and Wang R 2006 Acta Phys. Sin. 55 5733 (in Chinese)
[15]	Ma S J, Xu W and Fang T 2008 Nonlinear Dynamics 52 289
[16]	R?ssler O E 1976 Phys. Lett. A 57 397
[17]	Genesio R and Innocenti G 2008 Phys. Lett. A 372 1799
[18]	Vadivasova T E, Balanov A G, Sosnovtseva O V, Postnov D E and Mosekilde E 1999 Phys. Lett. A 253 66
[19]	Castro V, Monti M, Pardo W B and Walkenstein J A 2007 Int. J. Bifur. Chaos 17 965
[20]	Svetoslav N and Valko P 2004 Int. J. Bifur. Chaos 14 293
[21]	Jaume L and Claudia V 2007 Int. J. Bifur. Chaos 17 3289

[1]	Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter Xu Wei(徐伟), Ma Shao-Juan(马少娟), and Xie Wen-Xian(谢文贤). Chin. Phys. B, 2008, 17(3): 857-864.
[2]	Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer--van der Pol system Zhang Ying(张莹), Xu Wei(徐伟), Fang Tong(方同), and Xu Xu-Lin(徐旭林). Chin. Phys. B, 2007, 16(7): 1923-1933.
[3]	Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation Ma Shao-Juan (马少娟), Xu Wei (徐伟), Li Wei (李伟), Fang Tong (方同). Chin. Phys. B, 2006, 15(6): 1231-1238.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Stochastic period-doubling bifurcation analysis of a Rössler system with a bounded random parameter

Cite this article:

Online attention