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In this paper, we continue to study the chaotic characteristics of two curved surface mapping which forms a function in a unit area, and find that when one of the two curved surfaces is a standard curved surface and subjected to strong oscillation, and the other is randomly generate, the occurrence of chaos is more prone. Many different chaotic attractors are drawn by this method, adjusting the random surface to become subjective, the probability of chaotic attractor appearing can reach a half or more, which means that when certain conditions are meet, chaos is extremely common. Through calculating Lyapunov exponent and drawing the bifurcation diagram to analyze characteristics of chaos of the function, according to the bifurcation diagram of parameters and the Lyapunov exponent curve to look for more chaotic mapping function, a lot of chaotic attractors can be obtained. Finally a three-dimensional trigonometric function and two randomly generated three-dimensional polynomial functions are iterated, and many fancy three-dimensional attractors are obtained.
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Keywords:
- chaotic attractor /
- curved surface /
- iteration
[1] Li T Y, Yorke J A 1975 Am. Math. Mon. 82 984
[2] Oprocha P 2009 Nonlinear Anal. 71 5835
[3] He Y X, He Y L, Li H 1999 Comput. Graph. 23 547
[4] Viswanath D 2004 Physica D 190 115
[5] Kin D W, Chang P H 2013 Results Phys. 3 14
[6] Li C P, Chen G 2008 Chaos Solitons Fract. 18 807
[7] Reza M S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3857
[8] Yu W B, Zhou Y 2013 Acta Phys. Sin. 62 220501 (in Chinese) [于万波, 周洋 2013 物理学报 62 220501]
[9] Yu W B, Yang L Z 2013 Acta Phys. Sin. 62 020503 (in Chinese) [于万波, 杨灵芝 2013 物理学报 62 020503]
[10] Yu W B, Yang X S, Wei X P 2011 Application Research of Computers 28 3837 (in Chinese) [于万波, 杨雪松, 魏小鹏 2011 计算机应用研究 28 3837]
[11] Jin Y Q, Liang Z C 2003 Acta Phys. Sin. 52 1319 (in Chinese) [金亚秋, 梁子长 2003 物理学报 52 1319]
[12] Mo J Q, Lin W T 2000 Acta Phys. Sin. 49 1648 (in Chinese) [莫嘉琪, 林万涛 2000 物理学报 49 1648]
[13] Li C A 2005 Acta Phys. Sin. 54 1081 (in Chinese) [李传安 2005 物理学报 54 1081]
[14] Ge Y Z, Mi J C 2013 Acta Phys. Sin. 62 024704 (in Chinese) [戈阳祯, 米建春 2013 物理学报 62 024704]
[15] Yuan R S, Ma Y A, Yuan B, Ao P 2014 Chin. Phys. B 23 010505
[16] Gao W, Zha F S, Song B Y, Li M T 2014 Chin. Phys. B 23 010701
[17] Qin H, Xue P 2014 Chin. Phys. B 23 010301
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[1] Li T Y, Yorke J A 1975 Am. Math. Mon. 82 984
[2] Oprocha P 2009 Nonlinear Anal. 71 5835
[3] He Y X, He Y L, Li H 1999 Comput. Graph. 23 547
[4] Viswanath D 2004 Physica D 190 115
[5] Kin D W, Chang P H 2013 Results Phys. 3 14
[6] Li C P, Chen G 2008 Chaos Solitons Fract. 18 807
[7] Reza M S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3857
[8] Yu W B, Zhou Y 2013 Acta Phys. Sin. 62 220501 (in Chinese) [于万波, 周洋 2013 物理学报 62 220501]
[9] Yu W B, Yang L Z 2013 Acta Phys. Sin. 62 020503 (in Chinese) [于万波, 杨灵芝 2013 物理学报 62 020503]
[10] Yu W B, Yang X S, Wei X P 2011 Application Research of Computers 28 3837 (in Chinese) [于万波, 杨雪松, 魏小鹏 2011 计算机应用研究 28 3837]
[11] Jin Y Q, Liang Z C 2003 Acta Phys. Sin. 52 1319 (in Chinese) [金亚秋, 梁子长 2003 物理学报 52 1319]
[12] Mo J Q, Lin W T 2000 Acta Phys. Sin. 49 1648 (in Chinese) [莫嘉琪, 林万涛 2000 物理学报 49 1648]
[13] Li C A 2005 Acta Phys. Sin. 54 1081 (in Chinese) [李传安 2005 物理学报 54 1081]
[14] Ge Y Z, Mi J C 2013 Acta Phys. Sin. 62 024704 (in Chinese) [戈阳祯, 米建春 2013 物理学报 62 024704]
[15] Yuan R S, Ma Y A, Yuan B, Ao P 2014 Chin. Phys. B 23 010505
[16] Gao W, Zha F S, Song B Y, Li M T 2014 Chin. Phys. B 23 010701
[17] Qin H, Xue P 2014 Chin. Phys. B 23 010301
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