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In the paper, the chaotic characteristics of two functions are studied by a quadratic surface mapping in spatial unit area. When a surface is the standard surface in spatial unit area and another surface is generated randomly, the probability that the two functions are in the chaos can be greater than one-tenth, so this is a better method of generating chaos. The chaotic characteristics are analyzed by calculating the Lyapunov exponent and drawing the bifurcation diagram. According to the bifurcation diagram of the changing parameter and the characteristics of the regional distribution of the chaotic surface control points, the chaotic mapping function can be found and a lot of two-dimensional chaotic attractor graphics can be obtained. Besides, gray scale image is regarded as a discrete two-dimensional function for the first time. The study of image as an iteration expression shows some chaotic characteristics. The study shows that the same or similar image converges to the cycle point easily, which can be used in some research areas such as image recognition.
[1] Li T Y, York J A 1975 Am. Math. Monthly 82 984
[2] Chen X F, Chen G, Yu X 2000 Chaos Soliton. Fract. 10 771
[3] Chen Y C 2008 Int. J. Bifurc. Chaos 18 1825
[4] Liu H, Wang L D, Chu Z Y 2009 Nonlinear Anal. 71 6144
[5] Akhmet M U 2009 Math. Anal. Appl. 351 804
[6] Meng J D, Bao B C, Xu Q 2011 Acta Phys. Sin. 60 010504 (in Chinese) [孟继德, 包佰成, 徐强 2011 60 010504]
[7] Zhang Y S, Xiao D, Shu Y L, Li J 2013 Signal Process-Image 28 292
[8] Liu S X, Guan H Z, Yan H 2012 Acta Phys. Sin. 61 090506 (in Chinese) [刘诗序, 关宏志, 严海 2012 61 090506]
[9] Shi Y M, Chen G 2005 Int. J. Bifurc. Chaos 15 547
[10] Shu Y L 2008 Nonlinear Anal. 69 1768
[11] Aghababa M P 2012 Chin. Phys. B 21 100505
[12] Sun C C, Xu Q C, Sui Y 2013 Chin. Phys. B 22 030507
[13] Jiang G R, Xu B G, Yang Q G 2009 Chin. Phys. B 18 5235
[14] Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 0520
[15] Liu N, Guan Z H 2009 Chin. Phys. B 18 1769
[16] Yu W B, Wei X P 2006 Acta Phys. Sin. 55 3969 (in Chinese)[于万波, 魏小鹏 2006 55 3969]
[17] Yu W B, Yang L Z 2013 Acta Phys. Sin. 62 020503 (in Chinese) [于万波, 杨灵芝 2013 62 020503]
[18] Yu W B, Yang X S, Wei X P 2011 Appl. Res. Comput. 28 3837 (in Chinese) [于万波, 杨雪松, 魏小鹏 2011 计算机应用研究 28 3837]
[19] Yu W B, Yang L Z 2013 Comput. Engineer. 39 5 (in Chinese) [于万波, 杨灵芝 2013 计算机工程 39 5]
[20] Xu Z G, Tian Q, Tian L 2013 Acta Phys. Sin. 62 120501 (in Chinese) [徐正光, 田清, 田立 2013 62 120501]
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[1] Li T Y, York J A 1975 Am. Math. Monthly 82 984
[2] Chen X F, Chen G, Yu X 2000 Chaos Soliton. Fract. 10 771
[3] Chen Y C 2008 Int. J. Bifurc. Chaos 18 1825
[4] Liu H, Wang L D, Chu Z Y 2009 Nonlinear Anal. 71 6144
[5] Akhmet M U 2009 Math. Anal. Appl. 351 804
[6] Meng J D, Bao B C, Xu Q 2011 Acta Phys. Sin. 60 010504 (in Chinese) [孟继德, 包佰成, 徐强 2011 60 010504]
[7] Zhang Y S, Xiao D, Shu Y L, Li J 2013 Signal Process-Image 28 292
[8] Liu S X, Guan H Z, Yan H 2012 Acta Phys. Sin. 61 090506 (in Chinese) [刘诗序, 关宏志, 严海 2012 61 090506]
[9] Shi Y M, Chen G 2005 Int. J. Bifurc. Chaos 15 547
[10] Shu Y L 2008 Nonlinear Anal. 69 1768
[11] Aghababa M P 2012 Chin. Phys. B 21 100505
[12] Sun C C, Xu Q C, Sui Y 2013 Chin. Phys. B 22 030507
[13] Jiang G R, Xu B G, Yang Q G 2009 Chin. Phys. B 18 5235
[14] Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 0520
[15] Liu N, Guan Z H 2009 Chin. Phys. B 18 1769
[16] Yu W B, Wei X P 2006 Acta Phys. Sin. 55 3969 (in Chinese)[于万波, 魏小鹏 2006 55 3969]
[17] Yu W B, Yang L Z 2013 Acta Phys. Sin. 62 020503 (in Chinese) [于万波, 杨灵芝 2013 62 020503]
[18] Yu W B, Yang X S, Wei X P 2011 Appl. Res. Comput. 28 3837 (in Chinese) [于万波, 杨雪松, 魏小鹏 2011 计算机应用研究 28 3837]
[19] Yu W B, Yang L Z 2013 Comput. Engineer. 39 5 (in Chinese) [于万波, 杨灵芝 2013 计算机工程 39 5]
[20] Xu Z G, Tian Q, Tian L 2013 Acta Phys. Sin. 62 120501 (in Chinese) [徐正光, 田清, 田立 2013 62 120501]
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