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This paper aims to investigate an asymmetric bistable system driven by non-Gaussian Lvy noise. The stationary probability density functions are obtained by the Grnwald-Letnikov scheme, and the effects of noise intensity and stability index on the stationary probability density are examined. Phase transitions can be observed though a qualitative change of the stationary probability distribution, which indicates that the phase transitions are induced by the asymmetric parameter and the stability index of Lvy noise. Additionally, the mean first passage time is considered, and different mechanisms for the effects of asymmetric parameter, noise intensity and stability index on first passage time are also obtained.
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Keywords:
- non-Gaussian Lvy noise /
- asymmetric bistable system /
- phase transitions /
- mean first passage time
[1] Ushakov O,Wünsche H,Henneberger F,Khovanov I,Schimansky L,Zaks M A 2005 Phys. Rev. Lett. 95 123903
[2] Mankin R,Laas T,Sauga A,Ainsaar A,Reiter E 2006 Phys. Rev. E 74 021101
[3] Gan C B 2006 Nonlinear Dynamics 45 305
[4] Li J H, Huang Z Q 1997 Phys. Rev. E 53 3315
[5] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727(in Chinese)[杨建华、刘先斌 2010 59 3727]
[6] Han L B,Cao L,Wu D J,Wang J 2004 Acta Phys. Sin. 53 2127(in Chinese)[韩立波、曹 力、吴大进、王 俊 2004 53 2127]
[7] Xu Y, Gu R C, Zhang H Q, Xu W, Duan J Q 2011 Phys. Rev. E 83 056215
[8] Wan P, Zhan Y J, Li X C, Wang Y H 2011 Acta Phys. Sin. 60 040502(in Chinese)[万 频、詹宜巨、李学聪、王永华 2011 60 040502]
[9] Zhang X Y, Xu Wei, Zhou B C 2011 Acta Phys. Sin. 60 060514(in Chinese)[张晓燕、徐 伟、周丙常 2011 60 060514]
[10] Applebaum D 2009 Lévy Processes and Stochastic Calculus (Cambridge: Cambridge University Press) 2nd Edition
[11] Janicki A, Weron A 1994 Simulation and Chaotic Behavior of α-stable Stochastic Processes (New York:Marcel Dekker, INC)
[12] Dybiec B, Gudowaka-Nowak E, Sokolov I M 2007 Phys. Rev. E 76 041122
[13] Chechkin A V, Gonchar V Y, Klafter J, Netzler R 2006 Adv. Chem. Phys. 133 439
[14] Dubkov A A, Spagnolo B, Uchaikin V V 2008 Int. J. Bifurcation Chaos 18 2649
[15] Majumdar S N,Ziff R M 2008 Phys. Rev. Lett. 101 050601
[16] Romanelli A,Siri R,Micenmacher V 2007 Phys. Rev. E 76 037202
[17] Dybiec B,Gudowska E 2007 Phys. Rev. E 75 021109
[18] Ponomarev A V,Denisov S,Hanggi P 2010 Phys. Rev. A 81 043615
[19] Jin Y F,Xu W,Ma S J,Li W 2005 Acta Phys.Sin.54 2562(in Chinese)[靳艳飞、徐 伟、马少娟、李 伟 2005 54 3480]
[20] Zhang X Y, Xu W 2007 Chin. Phys.16 928
[21] Wang B,Wu X Q,Shao J H 2009 Acta Phys.Sin.58 1391(in Chinese)[王 兵、吴秀清、邵继红 2009 58 1391]
[22] Leccardi M 2005 ENOC’05(Fifth EUROMECH Nonlinear Dynamics Conference),Mini Symposium on Fractional Derivatives and Their Applications(Eindhoven,the Netherland)
[23] Podlubny I 1998 Fractional Differential Equations, Academic, San Diego
[24] Zeng L Z,Bao R H, Xu B H 2007 J. Phys. A: Math. Theor. 40 7175
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[1] Ushakov O,Wünsche H,Henneberger F,Khovanov I,Schimansky L,Zaks M A 2005 Phys. Rev. Lett. 95 123903
[2] Mankin R,Laas T,Sauga A,Ainsaar A,Reiter E 2006 Phys. Rev. E 74 021101
[3] Gan C B 2006 Nonlinear Dynamics 45 305
[4] Li J H, Huang Z Q 1997 Phys. Rev. E 53 3315
[5] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727(in Chinese)[杨建华、刘先斌 2010 59 3727]
[6] Han L B,Cao L,Wu D J,Wang J 2004 Acta Phys. Sin. 53 2127(in Chinese)[韩立波、曹 力、吴大进、王 俊 2004 53 2127]
[7] Xu Y, Gu R C, Zhang H Q, Xu W, Duan J Q 2011 Phys. Rev. E 83 056215
[8] Wan P, Zhan Y J, Li X C, Wang Y H 2011 Acta Phys. Sin. 60 040502(in Chinese)[万 频、詹宜巨、李学聪、王永华 2011 60 040502]
[9] Zhang X Y, Xu Wei, Zhou B C 2011 Acta Phys. Sin. 60 060514(in Chinese)[张晓燕、徐 伟、周丙常 2011 60 060514]
[10] Applebaum D 2009 Lévy Processes and Stochastic Calculus (Cambridge: Cambridge University Press) 2nd Edition
[11] Janicki A, Weron A 1994 Simulation and Chaotic Behavior of α-stable Stochastic Processes (New York:Marcel Dekker, INC)
[12] Dybiec B, Gudowaka-Nowak E, Sokolov I M 2007 Phys. Rev. E 76 041122
[13] Chechkin A V, Gonchar V Y, Klafter J, Netzler R 2006 Adv. Chem. Phys. 133 439
[14] Dubkov A A, Spagnolo B, Uchaikin V V 2008 Int. J. Bifurcation Chaos 18 2649
[15] Majumdar S N,Ziff R M 2008 Phys. Rev. Lett. 101 050601
[16] Romanelli A,Siri R,Micenmacher V 2007 Phys. Rev. E 76 037202
[17] Dybiec B,Gudowska E 2007 Phys. Rev. E 75 021109
[18] Ponomarev A V,Denisov S,Hanggi P 2010 Phys. Rev. A 81 043615
[19] Jin Y F,Xu W,Ma S J,Li W 2005 Acta Phys.Sin.54 2562(in Chinese)[靳艳飞、徐 伟、马少娟、李 伟 2005 54 3480]
[20] Zhang X Y, Xu W 2007 Chin. Phys.16 928
[21] Wang B,Wu X Q,Shao J H 2009 Acta Phys.Sin.58 1391(in Chinese)[王 兵、吴秀清、邵继红 2009 58 1391]
[22] Leccardi M 2005 ENOC’05(Fifth EUROMECH Nonlinear Dynamics Conference),Mini Symposium on Fractional Derivatives and Their Applications(Eindhoven,the Netherland)
[23] Podlubny I 1998 Fractional Differential Equations, Academic, San Diego
[24] Zeng L Z,Bao R H, Xu B H 2007 J. Phys. A: Math. Theor. 40 7175
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