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In this paper, we investigate the influence of each parameter of Willis chaotic system on the system, and calculate the Lyapunov exponent of Willis chaotic system containing chaotic phase. The analysis of the influence of chaotic phase on the Willis system shows that the random phase can control chaos. We also analyze the differences in intensity among various noises. Finally, the effectiveness of the above method is verified through the analysis of integrating phase portraits and Poincaré surface.
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Keywords:
- cerebral aneurysm /
- random phase /
- chaos control
[1] Austin G 1971 Math. Biosci. 11 163
[2] Hillen B, Hoogstraten H W, Post L 1986 J. Biomech. 19 187
[3] Nieto J J, Torres A 1995 J. Biol. Syst. 3 653
[4] Cao J D, Liu T Y 1993 J. Biomath. 8 9 (in Chinese) [曹进德, 刘天一 1993 生物数学学报 8 9]
[5] Nieto J J, Torres A 2000 J. Neurosci. 177 18
[6] Feng C H 1998 J. Biomath. 13 61 (in Chinese) [冯春华 1998 生物数学学报 13 61]
[7] Yang Q G, Jiang Y L 2000 J. Biomath. 15 313 (in Chinese) [杨启贵, 江佑霖 2000 生物数学学报 15 313]
[8] Yang C H, Zhu S M 2003 Acta Sci. Nat. Univ. Sunyatseni 42 1 (in Chinese) [杨翠红, 朱思铭 2003 中山大学学报(自然科学版) 42 1]
[9] Ott E, Grelogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[10] Guan X P, Fan Z P, Peng H P, He Y H 2001 J. Yanshan Univ. 25(Supl) 1 (in Chinese) [关新平, 范正平, 彭海鹏, 何宴辉 2001 燕山大学学报 25(Supl) 1]
[11] Zhou X A, Qian G B, Qiu S S 2006 Acta Phys. Sin. 55 3974 (in Chinese) [周小安, 钱恭斌, 丘水生 2006 55 3974]
[12] Yu H J, Zheng N 2007 Acta Phys. Sin. 56 3782 (in Chinese) [于洪洁, 郑宁 2007 56 3782]
[13] Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 54 3502]
[14] Zhang X D, Liu X D, Zheng Y, Liu C J 2013 Chin. Phys. B 22 030509
[15] Gholizadeh H, Hassannia A, Azarfar A 2013 Chin. Phys. B 22 010503
[16] Min F H, Ma M L 2013 Acta Phys. Sin. 62 210505 (in Chinese) [闵富红, 马美玲 2013 62 210505]
[17] Qu Z L, Hu G, Yang G J, Qin G 1995 Phys. Rev. Lett. 74 1736
[18] Lei Y M, Xu W, Xu Y, Fang T 2004 Chaos Solitons Fractals 21 1175
[19] Xu Y, Mahmoud G M, Xu W, Lei Y M 2005 Chaos Solitons Fractals 23 265
[20] Li S, Xu W, Li R H 2006 Acta Phys. Sin. 55 1049 (in Chinese) [李爽, 徐伟, 李瑞红 2006 55 1049]
[21] Li Y M, Yu S 2008 J. Biomath. 23 235 (in Chinese) [李医民, 于霜 2008 生物数学学报 23 235]
[22] Peng S H, Li D H, Su Z, Li H D 2010 Comput. Eng. Appl. 46 245 (in Chinese) [彭书华, 李邓化, 苏中, 李华德 2010 计算机工程与应用 46 245]
[23] Xiao J, Ma Z Z, Yang Y H 2013 Sci. World J. 2013 159194
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[1] Austin G 1971 Math. Biosci. 11 163
[2] Hillen B, Hoogstraten H W, Post L 1986 J. Biomech. 19 187
[3] Nieto J J, Torres A 1995 J. Biol. Syst. 3 653
[4] Cao J D, Liu T Y 1993 J. Biomath. 8 9 (in Chinese) [曹进德, 刘天一 1993 生物数学学报 8 9]
[5] Nieto J J, Torres A 2000 J. Neurosci. 177 18
[6] Feng C H 1998 J. Biomath. 13 61 (in Chinese) [冯春华 1998 生物数学学报 13 61]
[7] Yang Q G, Jiang Y L 2000 J. Biomath. 15 313 (in Chinese) [杨启贵, 江佑霖 2000 生物数学学报 15 313]
[8] Yang C H, Zhu S M 2003 Acta Sci. Nat. Univ. Sunyatseni 42 1 (in Chinese) [杨翠红, 朱思铭 2003 中山大学学报(自然科学版) 42 1]
[9] Ott E, Grelogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[10] Guan X P, Fan Z P, Peng H P, He Y H 2001 J. Yanshan Univ. 25(Supl) 1 (in Chinese) [关新平, 范正平, 彭海鹏, 何宴辉 2001 燕山大学学报 25(Supl) 1]
[11] Zhou X A, Qian G B, Qiu S S 2006 Acta Phys. Sin. 55 3974 (in Chinese) [周小安, 钱恭斌, 丘水生 2006 55 3974]
[12] Yu H J, Zheng N 2007 Acta Phys. Sin. 56 3782 (in Chinese) [于洪洁, 郑宁 2007 56 3782]
[13] Gong L H 2005 Acta Phys. Sin. 54 3502 (in Chinese) [龚礼华 2005 54 3502]
[14] Zhang X D, Liu X D, Zheng Y, Liu C J 2013 Chin. Phys. B 22 030509
[15] Gholizadeh H, Hassannia A, Azarfar A 2013 Chin. Phys. B 22 010503
[16] Min F H, Ma M L 2013 Acta Phys. Sin. 62 210505 (in Chinese) [闵富红, 马美玲 2013 62 210505]
[17] Qu Z L, Hu G, Yang G J, Qin G 1995 Phys. Rev. Lett. 74 1736
[18] Lei Y M, Xu W, Xu Y, Fang T 2004 Chaos Solitons Fractals 21 1175
[19] Xu Y, Mahmoud G M, Xu W, Lei Y M 2005 Chaos Solitons Fractals 23 265
[20] Li S, Xu W, Li R H 2006 Acta Phys. Sin. 55 1049 (in Chinese) [李爽, 徐伟, 李瑞红 2006 55 1049]
[21] Li Y M, Yu S 2008 J. Biomath. 23 235 (in Chinese) [李医民, 于霜 2008 生物数学学报 23 235]
[22] Peng S H, Li D H, Su Z, Li H D 2010 Comput. Eng. Appl. 46 245 (in Chinese) [彭书华, 李邓化, 苏中, 李华德 2010 计算机工程与应用 46 245]
[23] Xiao J, Ma Z Z, Yang Y H 2013 Sci. World J. 2013 159194
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