Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

doi:10.1088/1674-1056/25/9/090503

Abstract A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Hénon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Hénon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).

Keywords: chaotic map full state hybrid projective synchronization inverse problem maps with different dimensions

Received: 22 November 2015
Revised: 06 March 2016
Accepted manuscript online:

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

Corresponding Authors: Adel Ouannas, Giuseppe Grassi
E-mail: ouannas_adel@yahoo.fr;giuseppe.grassi@unisalento.it

Cite this article:

Adel Ouannas, Giuseppe Grassi Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions 2016 Chin. Phys. B 25 090503

[1]	Carroll T L and Pecora L M 1991 IEEE Trans. Circuits Syst. 38 453
[2]	Brucoli M, Carnimeo L and Grassi G 1996 Int. J. Bifurcat. Chaos 6 1673
[3]	Grassi G and Mascolo S 1997 IEEE Trans. Circuits Syst. I 44 1011
[4]	Grassi G and Mascolo S 1998 IEE Electron Lett. 34 424
[5]	Brucoli M, Cafagna D, Carnimeo L and Grassi G 1998 Int. J. Bifurcat. Chaos 8 2031
[6]	Grassi G and Mascolo S. 1999 IEEE Trans. Circuits Syst. II 46 478
[7]	Manieri R and Rehacek J 1999 Phys. Rev. Lett. 82 3042
[8]	Chee C Y and Xu D 2003 Phys. Lett. A 318 112
[9]	Xu D 2001 Phys. Rev. E 63 2
[10]	Xu D and Chee C Y 2002 Phys. Rev. E 66 046218
[11]	Grassi G and Miller D A 2009 Chaos Soliton. Fract. 39 1246
[12]	Grassi G and Miller D A 2007 Int. J. Bifur. Chaos 17 1337
[13]	Niu Y J, Wang X Y, Nian F Z and Wang M J 2010 Chin. Phys. B 19 120507
[14]	Hu M, Xu Z, Zhang R and Hu A 2007 Phys. Lett. A 365 315
[15]	Zhang Q and Lu J 2008 Phys. Lett. A 372 1416
[16]	Hu M, Xu Z, Zhang R and Hu A 2007 Phys. Lett. A 361 231
[17]	Hu M, Xu Z and Zhang R 2008 Comm. Nonlinear Science Num. Simulations 13 456
[18]	Hu M, Xu Z and Zhang R 2008 Comm. Nonlinear Science Num. Simulations 13 782
[19]	Grassi G 2012 Chin. Phys. B 21 060504
[20]	Han F, Wang Z J, Fan H and Gong T 2015 Chin. Phys. Lett. 32 40502
[21]	Wang S T, Wu Z M, Wu J G, Zhou L and Xia G Q 2015 Acta Phys. Sin. 64 154205 (in Chinese)
[22]	Ren H P and Bai C 2015 Chin. Phys. B 24 80503
[23]	Wei W and Zuo M 2015 Chin. Phys. B 24 80501
[24]	Liu S, Wang Z L, Zhao S S, Li H B and Xiong L J 2015 Chin. Phys. B 24 74501
[25]	Shu J 2015 Chin. Phys. B 24 60509
[26]	Yang F, Wang G Y and Wang X Y 2015 Chin. Phys. B 24 60506
[27]	Ouannas A 2014 J. Nonlinear Dynamics 983293
[28]	Ouannas A and Odibat Z 2015 Nonlinear Dynamics 81 765
[29]	Ouannas A and Mahmoud E E 2014 Journal Computational Intelligence and Electronic Systems 3 188
[30]	Danca M F and Tang W K S 2016 Chin. Phys. B 25 010505
[31]	Wang Y, Cai B Z, Jin P P and Hu T L 2016 Chin. Phys. B 25 010503
[32]	Hénon M 1976 Comm. Math. Phys. 50 69
[33]	Wang X Y 2003 Chaos in Complex Nonlinear Systems (Beijing: Publishing House of Electronics Industry)
[34]	Stefanski K 1998 Chaos Soliton. Fract. 9 83
[35]	Itoh M, Yang T and Chua L O 2001 Int. J. Bifurcation Chaos 11 551
[36]	Grassi G 2012 Chin. Phys. B 21 050505

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Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

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