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In the paper,a direct evidence for truncation error to complicate a simple system is provided,which proves the existence of anti-degradation mechanism in chaotic systems. Both one-dimensional circular arc iterated system and one-dimensional parabola iterated system are constructed,respectively. In each system,there is a non-hyperbolic fixed point. The corresponding iterative sequences are theoretically proved to be simple convergent sequences. However,there are a lot of iterative sequences that could jump over the fixed point in digital experiments. It is clearly revealed by digital-cell analysis that the topological variance of neighborhood of a non-hyperbolic fixed point is produced by truncation error,either a channel of type-I intermittency or a ripple bifurcation is configured from the fixed point.
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Keywords:
- truncation error /
- non-hyperbolic fixed point /
- anti-degradation mechanism /
- variance of topological configuration
[1] Baptista M S 1998 Phys. Lett. A 240 50
[2] Kocarev L,Jakimoski G 2001 Phys. Lett. A 289 199
[3] Stojanoski T,Kovarev L 2001 IEEE Trans. CAS-I 48 281
[4] Palacios A,Juarez H 2002 Phys. Lett. A 303 345
[5] Wang X M,Zhang J S,Zhang W F 2003 Acta Phys. Sin. 52 2737 (in Chinese) [王小敏、张家树、张文芳 2003 52 2737 ]
[6] Zhan H,Wang X F,Li C H,Liu D H 2005 Acta Phys. Sin. 54 4006 (in Chinese) [张 瀚、王秀峰、李朝晖、刘大海 2005 54 4006]
[7] Sheng L Y,Cao L L,Sun K H,Wen J 2005 Acta Phys. Sin. 54 4031 (in Chinese) [盛利元、曹莉凌、孙克辉、闻 姜 2005 54 4031]
[8] Wang L,Wang F P,Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 55 3964 ]
[9] Sheng L Y,Li G Q,Li Z W 2006 Acta Phys. Sin. 55 5700 (in Chinese) [盛利元、李更强、李志炜 2006 55 5700]
[10] Curiac D I,Iercan D,Dranga O,Dragan F,Banias O 2007 Proceedings of International Conference on Emerging Security Information,Systems and Technologies (SECURWARE 2007),Valencia,Spain,October 14—20,2007 p71
[11] Levy Y E 1982 Phys. Lett. A 53 1
[12] Beck C,Roepstorff G 1987 Physica D 25 173
[13] Binder P M 1992 Physica 57 31
[14] Li S J,Mou X Q,Cai Y L,Ji Z,Zhang J H 2003 Comput. Phys. Commun. 153 52
[15] Alvarez G,Li S J 2006 Int. J. Bifurc. Chaos. 16 2129
[16] Sheng L Y,Wen J,Cao L L,Xiao Y Y 2007 Acta Phys. Sin. 56 0078 (in Chinese) [盛利元、闻 姜、曹莉凌、肖燕予 2007 56 0078]
[17] Sheng L Y,Jia W Y 2005 Acta Phys. Sin. 54 5574 (in Chinese) [盛利元、贾伟尧 2005 54 5574]
[18] Sheng L Y,Jia W Y,Wu S C,Xia G R 2007 Acta Phys. Sin. 56 3753 (in Chinese) [盛利元、贾伟尧、吴舒辞、夏国荣 2007 56 3753]
[19] Murakami K 2005 J. Math. Anal. Appl. 310 492
[20] Li S J 2003 Ph. D. Dissertation (Xian:Xian Jiaotong University) (in Chinese) [李树钧 2003 博士学位论文(西安:西安交通大学)]
[21] Pomeau Y,Manneville P 1980 Commun. Math. Phys. 74 189
[22] Oteo J A,Ros J 2007 Phys. Rev. E 76 036214
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[1] Baptista M S 1998 Phys. Lett. A 240 50
[2] Kocarev L,Jakimoski G 2001 Phys. Lett. A 289 199
[3] Stojanoski T,Kovarev L 2001 IEEE Trans. CAS-I 48 281
[4] Palacios A,Juarez H 2002 Phys. Lett. A 303 345
[5] Wang X M,Zhang J S,Zhang W F 2003 Acta Phys. Sin. 52 2737 (in Chinese) [王小敏、张家树、张文芳 2003 52 2737 ]
[6] Zhan H,Wang X F,Li C H,Liu D H 2005 Acta Phys. Sin. 54 4006 (in Chinese) [张 瀚、王秀峰、李朝晖、刘大海 2005 54 4006]
[7] Sheng L Y,Cao L L,Sun K H,Wen J 2005 Acta Phys. Sin. 54 4031 (in Chinese) [盛利元、曹莉凌、孙克辉、闻 姜 2005 54 4031]
[8] Wang L,Wang F P,Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 55 3964 ]
[9] Sheng L Y,Li G Q,Li Z W 2006 Acta Phys. Sin. 55 5700 (in Chinese) [盛利元、李更强、李志炜 2006 55 5700]
[10] Curiac D I,Iercan D,Dranga O,Dragan F,Banias O 2007 Proceedings of International Conference on Emerging Security Information,Systems and Technologies (SECURWARE 2007),Valencia,Spain,October 14—20,2007 p71
[11] Levy Y E 1982 Phys. Lett. A 53 1
[12] Beck C,Roepstorff G 1987 Physica D 25 173
[13] Binder P M 1992 Physica 57 31
[14] Li S J,Mou X Q,Cai Y L,Ji Z,Zhang J H 2003 Comput. Phys. Commun. 153 52
[15] Alvarez G,Li S J 2006 Int. J. Bifurc. Chaos. 16 2129
[16] Sheng L Y,Wen J,Cao L L,Xiao Y Y 2007 Acta Phys. Sin. 56 0078 (in Chinese) [盛利元、闻 姜、曹莉凌、肖燕予 2007 56 0078]
[17] Sheng L Y,Jia W Y 2005 Acta Phys. Sin. 54 5574 (in Chinese) [盛利元、贾伟尧 2005 54 5574]
[18] Sheng L Y,Jia W Y,Wu S C,Xia G R 2007 Acta Phys. Sin. 56 3753 (in Chinese) [盛利元、贾伟尧、吴舒辞、夏国荣 2007 56 3753]
[19] Murakami K 2005 J. Math. Anal. Appl. 310 492
[20] Li S J 2003 Ph. D. Dissertation (Xian:Xian Jiaotong University) (in Chinese) [李树钧 2003 博士学位论文(西安:西安交通大学)]
[21] Pomeau Y,Manneville P 1980 Commun. Math. Phys. 74 189
[22] Oteo J A,Ros J 2007 Phys. Rev. E 76 036214
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