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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.
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Keywords:
- chaos /
- random phase /
- stochastic resonance /
- Lyapunov exponent
[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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[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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