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Generalized synchronization between different chaotic maps via dead-beat control |
Grassi G† |
Dipartimento di Ingegneria dell'Innovazione, Università del Salento, Lecce 73100, Italy |
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Abstract This paper presents a new scheme to achieve generalized synchronization (GS) between different discrete-time chaotic (hyperchaotic) systems. The approach is based on a theorem, which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied. The method presents some useful features:it enables exact GS to be achieved in finite time (i.e., dead-beat synchronization); it is rigorous, systematic, and straightforward in checking GS; it can be applied to a wide class of chaotic maps. Some examples of GS, including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map, are illustrated.
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Received: 15 November 2011
Revised: 27 April 2012
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Xt
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(Synchronization; coupled oscillators)
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Cite this article:
Grassi G Generalized synchronization between different chaotic maps via dead-beat control 2012 Chin. Phys. B 21 050505
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[1] |
Chen G and Ueta T (eds) 2002 Chaos in Circuits and Systems (Singapore:World Scientific Publishing Co.) p. 1
|
[2] |
Grassi G 2008 Chin. Phys. B 17 3247
|
[3] |
Carroll T L and Pecora L M 1990 Phys. Rev. Lett. 64 821
|
[4] |
Brucoli M, Carnimeo L and Grassi G 1996 Int. J. Bifurcat. Chaos 6 1673
|
[5] |
Grassi G and Mascolo S 1997 IEEE T. Circ. Syst. I 44 1011
|
[6] |
Mascolo S and Grassi G 1997 Phys. Rev. E 56 6166
|
[7] |
Grassi G and Mascolo S 1998 IEE Electron. Lett. 34 424
|
[8] |
Brucoli M, Cafagna D, Carnimeo L and Grassi G 1998 Int. J. Bifurcat. Chaos 8 2031
|
[9] |
Grassi G and Mascolo S 1999 IEEE T. Circ. Syst. I 46 1135
|
[10] |
Grassi G and Mascolo S 1999 IEEE T. Circ. Syst. II 46 478
|
[11] |
Miller D A and Grassi G 2001 IEEE T. Circ. Syst. I 48 366
|
[12] |
Grassi G and Miller D A 2002 IEEE T. Circ. Syst. I 49 373
|
[13] |
Sang J Y, Yang J and Yue L J 2011 Chin.Phys. B 20 080507
|
[14] |
Grassi G and Miller D A 2007 Int. J. Bifurcat. Chaos 17 1337
|
[15] |
Zhang R and Xu Z Y 2010 Chin. Phys. B 19 120511
|
[16] |
Hu M, Xu Z and Zhang R 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 782
|
[17] |
Grassi G and Miller D A 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 1824
|
[18] |
Rulkov N F, Sushchik M M, Tsimring L S and Abarbanel H D I 1995 Phys. Rev. E 51 980
|
[19] |
Kocarev L and Parlitz U 1996 Phys. Rev. Lett. 76 1816
|
[20] |
Abarbanel H D I, Rulkov N F and Sushchik M M 1996 Phys. Rev. E 53 4528
|
[21] |
Ho M C and Hung Y C 2002 Phys. Lett. A 301 424
|
[22] |
Li G H 2007 Chin. Phys. 16 2608
|
[23] |
Li G H 2009 Chaos Soliton. Fract. 39 2056
|
[24] |
Niu Y J, Wang X Y, Nian F Z and Wang M J 2010 Chin. Phys. B 19 120507-1
|
[25] |
Dai H, Jia L X, Hui M and Si G Q 2011 Chin. Phys. B 20 040507-1
|
[26] |
Rulkov N F, Afraimovich V S, Lewis C T, Chazottes J R and Cordonet A 2001 Phys. Rev. E 64 016217
|
[27] |
So P, Barreto E, Josic K, Sander E and Schiff S J 2002 Phys. Rev. E 65 046225
|
[28] |
Hramov A E and Koronovskii A A 2005 Phys. Rev. E 71 067201
|
[29] |
Jing J Y and Min L Q 2009 Commun. Theor. Phys. 51 1149
|
[30] |
Yuan Z, Xu Z and Guo L 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 992
|
[31] |
Zeraoulia E and Sprott J C 2008 Int. J. Bifurcat. Chaos 18 1567
|
[32] |
Grassi G 2010 J. Fraklin I. 347 438
|
[33] |
Zeraoulia E and Sprott J C 2009 Int. J. Bifurcat. Chaos 19 1023
|
[34] |
Dorf R C and Bishop R H 2005 Modern Control Systems (Upper Saddle River:Prentice Hall) p. 69
|
[35] |
Grassi G and Miller D A 2009 Chaos Soliton. Fract. 39 1246
|
[36] |
Afraimovich V S, Cordonet A and Rulkov N F 2002 Phys. Rev. E 66 016208
|
[37] |
Baier G and Klein M 1990 Phys. Lett. A 151 281
|
[38] |
Yang X S and Chen G 2002 Chaos Soliton. Fract. 13 1303
|
[39] |
Lu J 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 1851
|
[40] |
Ji Y, Liu T and Min L 2008 Phys. Lett. A 372 3645
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