Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal

doi:10.1088/1674-1056/22/8/080505

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80505-080505.doi: 10.1088/1674-1056/22/8/080505

Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal

Giuseppe Grassi

Dipartimento Ingegneria Innovazione, Universitá del Salento-73100 Lecce, Italy

收稿日期:2012-12-04 修回日期:2013-01-12 出版日期:2013-06-27 发布日期:2013-06-27

Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal

Giuseppe Grassi

Dipartimento Ingegneria Innovazione, Universitá del Salento-73100 Lecce, Italy

Received:2012-12-04 Revised:2013-01-12 Online:2013-06-27 Published:2013-06-27
Contact: Giuseppe Grassi E-mail:giuseppe.grassi@unisalento.it

摘要/Abstract

摘要： Referring to continuous-time chaotic systems, this paper presents a new projective synchronization scheme, which enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic (hyperchaotic) systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.

关键词: continuous-time chaotic systems, chaos synchronization, observer-based synchronization, scalar synchronizing signal

Abstract: Referring to continuous-time chaotic systems, this paper presents a new projective synchronization scheme, which enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic (hyperchaotic) systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.

Key words: continuous-time chaotic systems, chaos synchronization, observer-based synchronization, scalar synchronizing signal

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Xt (Synchronization; coupled oscillators)

Giuseppe Grassi. Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal[J]. 中国物理B, 2013, 22(8): 80505-080505.

Giuseppe Grassi. Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal[J]. Chin. Phys. B, 2013, 22(8): 80505-080505.

参考文献 23

[1]	Li Y and Liu Z R 2010 Chin. Phys. B 19 110501
[2]	Carroll T L and Pecora L M 1991 IEEE Trans. Circ. Sys. 38 453
[3]	Grassi G and Mascolo S 1999 IEEE Trans. Circ. Sys. I46 1135
[4]	Grassi G and Mascolo S 1999 Int. J. Circ. Theory Appl. 27 543
[5]	Grassi G and Mascolo S 1997 IEEE Trans. Circ. Sys. I44 1011
[6]	Grassi G and S. Mascolo 1999 IEEE Trans. Circ. Sys. II46 478
[7]	Grassi G and Mascolo S 1998 IEE Electron. Lett. 34 424
[8]	Miller D A and Grassi G 2001 IEEE Trans. Circ. Sys. I48 366
[9]	Brucoli, M, Carnimeo L and Grassi G 1996 Int. J. Bifur. Chaos 6 1673
[10]	Brucoli, M, Carnimeo L and Grassi G 1996 Int. J. Circ. Theory Appl. 24 489
[11]	Mainieri R and Rehacek J 1999 Phys. Rev. Lett. 82 3042
[12]	Grassi G and Miller D A 2009 Chaos, Solitons & Fractals 39 1246
[13]	Grassi G and Miller D A 2007 Int. J. Bifur. Chaos 17 1337
[14]	Hu M, Xu Z, Zhang R and Hu A 2007 Phys. Lett. A 361 231
[15]	Hu M, Xu Z and Zhang R 2008 Commun. Nonlinear Sci. Numer. Simul. 13 456
[16]	Hu M, Xu Z and Zhang R 2008 Commun. Nonlinear Sci. Numer. Simul. 13 782
[17]	Dai H, Jia L X, Hui M and Si G Q 2011 Chin. Phys. B 20 040507
[18]	Grassi G 2012 Chin. Phys. B 21 060504
[19]	Chu Y D, Chang Y X, An X L, Yu J N and Zhang J G 2011 Commun. Nonlinear Sci. Numer. Simul. 16 1509
[20]	Tang W K S, Zhong G Q, Chen G and Man K F 2001 IEEE Trans. Circ. Sys. I48 1369
[21]	Grassi G and Vecchio P 2007 Dynamics of Continuous, Discrete and Impulsive Systems B 14 705
[22]	Grassi G and Grieco LA 2003 IEEE Trans. Circ. Sys. I50 488
[23]	Guo L X, Xu Z Y and Hu M F 2008 Chin. Phys. B 17 4067

Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal

Continuous-time chaotic systems：Arbitrary full-state hybrid projective synchronization via a scalar signal

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