Generalized synchronization between different chaotic maps via dead-beat control

doi:10.1088/1674-1056/21/5/050505

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.

Keywords: generalized synchronization chaos synchronization discrete-time chaotic systems dead-beat control chaotic maps

Received: 15 November 2011
Revised: 27 April 2012
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Xt	(Synchronization; coupled oscillators)

Cite this article:

Grassi G Generalized synchronization between different chaotic maps via dead-beat control 2012 Chin. Phys. B 21 050505

[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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