Duffing系统随机相位抑制混沌与随机共振并存现象的机理研究

李爽; 李倩; 李佼瑞

doi:10.7498/aps.64.100501

摘要

针对随机相位作用的Duffing混沌系统, 研究了随机相位强度变化时系统混沌动力学的演化行为及伴随的随机共振现象. 结合Lyapunov指数、庞加莱截面、相图、时间历程图、功率谱等工具, 发现当噪声强度增大时, 系统存在从混沌状态转化为有序状态的过程, 即存在噪声抑制混沌的现象, 且在这一过程中, 系统亦存在随机共振现象, 而且随机共振曲线上最优的噪声强度恰为噪声抑制混沌的参数临界点. 通过含随机相位周期力的平均效应分析并结合系统的分岔图, 探讨了噪声对混沌运动演化的作用机理, 解释了在此过程中随机共振的形成机理, 论证了噪声抑制混沌与随机共振的相互关系.

关键词:

Abstract

Noise, which is ubiquitous in real systems, has been the subject of various and extensive studies in nonlinear dynamical systems. In general, noise is regarded as an obstacle. However, counterintuitive effects of noise on nonlinear systems have recently been recognized, such as noise suppressing chaos and stochastic resonance. Although the noise suppressing chaos and stochastic resonance have been studied extensively, little is reported about their relation under coexistent condition. In this paper by using Lyapunov exponent, Poincaré section, time history and power spectrum, the effect of random phase on chaotic Duffing system is investigated. It is found that as the intensity of random phase increases the chaotic behavior is suppressed and the power response amplitude passes through a maximum at an optimal noise intensity, which implies that the coexistence phenomenon of noise suppressing chaos and stochastic resonance occurs. Furthermore, an interesting phenomenon is that the optimal noise intensity at the SR curve is just the critical point from chaos to non-chaos. The average effect analysis of harmonic excitation with random phase and the system’s bifurcation diagram shows that the increasing of random phase intensity is in general equivalent to the decreasing of harmonic excitation amplitude of the original deterministic system. So there exists the critical noise intensity where the chaotic motion of large range disintegrates and non-chaotic motion of small scope appears, which implies the enhancing of the regularity of system motion and the increasing of the response amplitude at the input signal frequency. After that, the excess noise will not change the stability of the system any more, but will increase the degree of random fluctuation near the stable motion, resulting in the decreasing of the response amplitude. Therefore, the formation of stochastic resonance is due to the dynamical mechanism of random phase suppressing chaos.

Keywords:

作者及机构信息

1.
西安财经学院统计学院, 西安 710100;

2.
陕西科技大学设计与艺术学院, 西安 710021

基金项目: 国家自然科学基金(批准号: 11202155)、陕西省教育厅基金(批准号:2013JK0595)和陕西省自然科学基金(批准号: 2014JQ9372)资助的课题.

Authors and contacts

1.
School of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, China;

2.
College of Art and Design, Shaanxi University of Science and Technology, Xi’an 710021, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11202155), the Education Department Foundation of Shaanxi, China (Grant No. 2013JK0595), and the Natural Science Foundation of Shaanxi, China (Grant No. 2014JQ9372).

参考文献

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[2]	Ramesh M, Narayanan S 1999 Chaos, Soliton. Fract. 10 1473
[3]	Yang X L, Xu W 2009 Acta Phys. Sin. 58 3722 (in Chinese) [杨晓丽, 徐伟 2009 物理学报 58 3722]
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[5]	Yoshimoto M, Shirahama H, Kurosawa S 2008 J. Chem. Phys. 129 014508
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[7]	Xu Y, Mahmoud G M, Xu W, Lei Y M 2005 Chaos, Soliton. Fract. 23 265
[8]	Li S, Xu W, Li R H 2006 Acta Phys. Sin. 55 1049 (in Chinese) [李爽, 徐伟, 李瑞红 2006 物理学报 55 1049]
[9]	Gu Y F, Xiao J 2014 Acta Phys. Sin. 63 160506 (in Chinese) [古元凤, 肖剑 2014 物理学报 63 160506]
[10]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
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[13]	Arathi S, Rajasekar S 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 4049
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[15]	Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
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施引文献

[1]	Matsumoto K, Tsuda I 1983 J. Stat. Phys. 31 87
[2]	Ramesh M, Narayanan S 1999 Chaos, Soliton. Fract. 10 1473
[3]	Yang X L, Xu W 2009 Acta Phys. Sin. 58 3722 (in Chinese) [杨晓丽, 徐伟 2009 物理学报 58 3722]
[4]	Wei J G, Leng G 1997 Appl. Math. Comput. 88 77
[5]	Yoshimoto M, Shirahama H, Kurosawa S 2008 J. Chem. Phys. 129 014508
[6]	Lei Y M, Xu W, Xu Y, Fang T 2004 Chaos, Soliton. Fract. 21 1175
[7]	Xu Y, Mahmoud G M, Xu W, Lei Y M 2005 Chaos, Soliton. Fract. 23 265
[8]	Li S, Xu W, Li R H 2006 Acta Phys. Sin. 55 1049 (in Chinese) [李爽, 徐伟, 李瑞红 2006 物理学报 55 1049]
[9]	Gu Y F, Xiao J 2014 Acta Phys. Sin. 63 160506 (in Chinese) [古元凤, 肖剑 2014 物理学报 63 160506]
[10]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[11]	Zhang G J, Xu J X 2005 Chaos, Soliton. Fract. 27 1056
[12]	Jngling T, Benner H, Stemler T, Just W 2008 Phys. Rev. E 77 036216
[13]	Arathi S, Rajasekar S 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 4049
[14]	Lu K, Wang F Z, Zhang G L, Fu W H 2013 Chin. Phys. B 22 120202
[15]	Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[16]	Wang K K, Liu X B 2014 Chin. Phys. B 23 010502
[17]	Yamazaki H, Yamada T, Kai S 1998 Phys. Rev. Lett. 81 4112
[18]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[19]	Qian M, Zhang X J 2001 Phys. Rev. E 65 011101
[20]	Zhang X J 2004 J. Phys. A: Math. Gen. 37 7473

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