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In this paper, a class of wide range Julia set of parameter identification problem is investigated. Based on the nonlinear feedback controller and the discretized equation theory, the designed generally applicable adaptive synchronization controller and the parameter adaptive law are obtained, and it is proved that the designed controller of generalized Julia set can achieve the synchronization. Moreover, it can identify the unknown parameters of the generalized Julia set. Particularly, the parameter identification of the basic form of Julia set is discussed in the paper.
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Keywords:
- Julia set /
- synchronization /
- parameter identification
[1] Halsey T C, Jensen M H, Kadanoff L P 1986 Phys.Rev.A 33 1141
[2] Li Y,Kong X M,Huang J Y 2002 Acta Phys. Sin. 51 1346(in Chinese)\[李 英、孔祥木、黄家寅 2002 51 1346]
[3] Yu H S,Sun X,Luo S F,Wu Z Q 2002 Acta Phys. Sin. 51 999(in Chinese)\[于会生、孙 霞、罗守福、吴自勤 2002 51 999]
[4] He T,Zhou Z O 2007 Acta Phys. Sin. 56 693(in Chinese)\[贺 涛、周正欧 2007 56 693]
[5] Sun X,Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese)\[孙 霞、吴自勤 2001 50 2126]
[6] Falconer K 1990 Fractals Geometry Mathematical Foundations and Applications (New York: Wiley)
[7] Rammal R 1984 J. de Phys. ( Paris: The TeXbook)p191—206.
[8] Biskup M, Borgs C, Chayes J 2000 Phys. Rev. Lett. 84 4794
[9] Wang L,Zheng D Z 2000 Control Theory and Applications 17 139(in Chinese)\[王 凌、郑大钟 2000 控制理论与应用 17 139]
[10] Wang X Y,Meng Q Y 2004 Acta Phys. Sin. 53 388 (in Chinese) \[王兴元、孟庆业 2004 53 388]
[11] Li S 2000 In: 5th International conference on signal processing proceeding. (Beijing: Publing House Electronic Industry) p285
[12] Lakhtakia A 1987 J. Phys A Math. Gen. 20 3533
[13] Zhang Y P, Liu S T, Shen S L 2009 Chaos Solitons and Fractals 39 1811
[14] Liu S T, Zhang Y P 2008 Acta Phys. Sin. 57 737(in Chinese)\[刘树堂、张永平 2008 57 737]
[15] Jia Z Q 2001 Higher mathematics(2)(Beijing: Science publisher)p199—200 (inChinese) \[贾启禹 2001 高等数学(下)(北京: 科学出版社)第199—200 页]
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[1] Halsey T C, Jensen M H, Kadanoff L P 1986 Phys.Rev.A 33 1141
[2] Li Y,Kong X M,Huang J Y 2002 Acta Phys. Sin. 51 1346(in Chinese)\[李 英、孔祥木、黄家寅 2002 51 1346]
[3] Yu H S,Sun X,Luo S F,Wu Z Q 2002 Acta Phys. Sin. 51 999(in Chinese)\[于会生、孙 霞、罗守福、吴自勤 2002 51 999]
[4] He T,Zhou Z O 2007 Acta Phys. Sin. 56 693(in Chinese)\[贺 涛、周正欧 2007 56 693]
[5] Sun X,Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese)\[孙 霞、吴自勤 2001 50 2126]
[6] Falconer K 1990 Fractals Geometry Mathematical Foundations and Applications (New York: Wiley)
[7] Rammal R 1984 J. de Phys. ( Paris: The TeXbook)p191—206.
[8] Biskup M, Borgs C, Chayes J 2000 Phys. Rev. Lett. 84 4794
[9] Wang L,Zheng D Z 2000 Control Theory and Applications 17 139(in Chinese)\[王 凌、郑大钟 2000 控制理论与应用 17 139]
[10] Wang X Y,Meng Q Y 2004 Acta Phys. Sin. 53 388 (in Chinese) \[王兴元、孟庆业 2004 53 388]
[11] Li S 2000 In: 5th International conference on signal processing proceeding. (Beijing: Publing House Electronic Industry) p285
[12] Lakhtakia A 1987 J. Phys A Math. Gen. 20 3533
[13] Zhang Y P, Liu S T, Shen S L 2009 Chaos Solitons and Fractals 39 1811
[14] Liu S T, Zhang Y P 2008 Acta Phys. Sin. 57 737(in Chinese)\[刘树堂、张永平 2008 57 737]
[15] Jia Z Q 2001 Higher mathematics(2)(Beijing: Science publisher)p199—200 (inChinese) \[贾启禹 2001 高等数学(下)(北京: 科学出版社)第199—200 页]
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