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In this paper, the spatial-alternated Julia sets are discussed, which are obtained by alternated iteration of quadratic family zm+1,n+azm,n+1=(1+a)2zmn2+ci,i=1,2. The control of spatial-alternated Julia sets is accomplished by using the feedback control. Then the linear generalized synchronization of two different spatial-alternated Julia sets is discussed. The simulations demonstrate the effectiveness of the control methods.
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Keywords:
- spatial-alternated Julia sets /
- the feedback control /
- synchronization /
- the linear generalized synchronization
[1] Romera M, Ppstor G 2009 Int. J. Bifurcat. Chaos 6 2123
[2] Sui S G 2005 M. S. Dissertation (Jinan: Shandong University) (in Chinese) [隋首钢 2005 硕士学位论文 (济南: 山东大学)]
[3] Liu S T, Zhang Y P 2008 Acta Phys. Sin. 57 737 (in Chinese) [刘树堂, 张永平 2008 57 737]
[4] Qin W Y, Sun T, Jiao X D, Yang Y F 2012 Acta Phys. Sin. 61 090502 (in Chineses) [秦卫阳, 孙涛, 焦旭东, 杨永锋 2012 61 090502]
[5] Liu P, Liu S T 2011 Commun. Nonlinear Sci. Number Simulat. 16 3344
[6] Liu P, Liu C A 2011 Int. J. Bifurcat. Chaos 21 1281
[7] Liu S T, Chen G R 2003 Int. J. Bifurcat. Chaos 13 1163
[8] Zhang Y P, Liu S T 2008 Chin. Phys. B 17 543
[9] Blanchard P, Devaney R, Keen L 2004 Proc. Symp. Appl. Math. 60 37
[10] Lakhtakia A, Varadan V V, Messier R, Varadan V K 1987 J. Phys. A: Math. Gen. 20 3533
[11] Goldberger A L, Amaral L A, Hausdorff J M, Ivanov P C, Peng C K, Stanley H E 2002 Proc. Nat. Acad. Sci. 99 2466
[12] Ascencio S F, Meana H P, Miyatake M N 2001 Phys. Engineer. Millim. Sub-Millim. Waves 1 241
[13] Tamasevicius A 1997 Electr. Lett. 33 1105
[14] Blasius B, Huppert A, Stone L 1999 Nature 399 354
[15] Liu S T, Wu S, Zhang Y P 2006 Int. J. Bifurcat. Chaos 16 2697
[16] Liang X, Zhang J, Xia X 2008 IEEE Trans. Autom. Control 53 1740
[17] Danca M F, Tang W, Chen G 2008 Appl. Math. Comput. 201 650
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[1] Romera M, Ppstor G 2009 Int. J. Bifurcat. Chaos 6 2123
[2] Sui S G 2005 M. S. Dissertation (Jinan: Shandong University) (in Chinese) [隋首钢 2005 硕士学位论文 (济南: 山东大学)]
[3] Liu S T, Zhang Y P 2008 Acta Phys. Sin. 57 737 (in Chinese) [刘树堂, 张永平 2008 57 737]
[4] Qin W Y, Sun T, Jiao X D, Yang Y F 2012 Acta Phys. Sin. 61 090502 (in Chineses) [秦卫阳, 孙涛, 焦旭东, 杨永锋 2012 61 090502]
[5] Liu P, Liu S T 2011 Commun. Nonlinear Sci. Number Simulat. 16 3344
[6] Liu P, Liu C A 2011 Int. J. Bifurcat. Chaos 21 1281
[7] Liu S T, Chen G R 2003 Int. J. Bifurcat. Chaos 13 1163
[8] Zhang Y P, Liu S T 2008 Chin. Phys. B 17 543
[9] Blanchard P, Devaney R, Keen L 2004 Proc. Symp. Appl. Math. 60 37
[10] Lakhtakia A, Varadan V V, Messier R, Varadan V K 1987 J. Phys. A: Math. Gen. 20 3533
[11] Goldberger A L, Amaral L A, Hausdorff J M, Ivanov P C, Peng C K, Stanley H E 2002 Proc. Nat. Acad. Sci. 99 2466
[12] Ascencio S F, Meana H P, Miyatake M N 2001 Phys. Engineer. Millim. Sub-Millim. Waves 1 241
[13] Tamasevicius A 1997 Electr. Lett. 33 1105
[14] Blasius B, Huppert A, Stone L 1999 Nature 399 354
[15] Liu S T, Wu S, Zhang Y P 2006 Int. J. Bifurcat. Chaos 16 2697
[16] Liang X, Zhang J, Xia X 2008 IEEE Trans. Autom. Control 53 1740
[17] Danca M F, Tang W, Chen G 2008 Appl. Math. Comput. 201 650
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