Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

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

中国物理B ›› 2016, Vol. 25 ›› Issue (9): 90503-090503.doi: 10.1088/1674-1056/25/9/090503

Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

Adel Ouannas, Giuseppe Grassi

1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa 12002, Algeria;
2 Università del Salento, Dipartimento Ingegneria Innovazione, 73100 Lecce, Italy

收稿日期:2015-11-22 修回日期:2016-03-06 出版日期:2016-09-05 发布日期:2016-09-05
通讯作者: Adel Ouannas, Giuseppe Grassi E-mail:ouannas_adel@yahoo.fr;giuseppe.grassi@unisalento.it

Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

Adel Ouannas¹, Giuseppe Grassi²

1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa 12002, Algeria;
2 Università del Salento, Dipartimento Ingegneria Innovazione, 73100 Lecce, Italy

Received:2015-11-22 Revised:2016-03-06 Online:2016-09-05 Published:2016-09-05
Contact: Adel Ouannas, Giuseppe Grassi E-mail:ouannas_adel@yahoo.fr;giuseppe.grassi@unisalento.it

摘要/Abstract

摘要： 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).

关键词: chaotic map, full state hybrid projective synchronization, inverse problem, maps with different dimensions

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).

Key words: chaotic map, full state hybrid projective synchronization, inverse problem, maps with different dimensions

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Xt (Synchronization; coupled oscillators)

Adel Ouannas, Giuseppe Grassi. Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions[J]. 中国物理B, 2016, 25(9): 90503-090503.

Adel Ouannas, Giuseppe Grassi. Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions[J]. Chin. Phys. B, 2016, 25(9): 90503-090503.

参考文献 36

[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

Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 36

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Guo-Dong Ye(叶国栋), Hui-Shan Wu(吴惠山), Xiao-Ling Huang(黄小玲), and Syh-Yuan Tan. Asymmetric image encryption algorithm based ona new three-dimensional improved logistic chaotic map[J]. 中国物理B, 2023, 32(3): 30504-030504.
[2]	Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). A color image encryption algorithm based on hyperchaotic map and DNA mutation[J]. 中国物理B, 2023, 32(3): 30501-030501.
[3]	Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). A novel hyperchaotic map with sine chaotification and discrete memristor[J]. 中国物理B, 2022, 31(12): 120501-120501.
[4]	彭越兮, 孙克辉, 贺少波. Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm[J]. 中国物理B, 2020, 29(3): 30502-030502.
[5]	陈琳, 郑志伟, 包立君, 方金生, 杨天和, 蔡淑惠, 蔡聪波. Weighted total variation using split Bregman fast quantitative susceptibility mapping reconstruction method[J]. 中国物理B, 2018, 27(8): 88701-088701.
[6]	刘泽宇, 夏铁成, 王金波. Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem[J]. 中国物理B, 2018, 27(3): 30502-030502.
[7]	陈天宇, 陈阳, 杨胡江, 肖井华, 胡岗. Reconstruction of dynamic structures of experimental setups based on measurable experimental data only[J]. 中国物理B, 2018, 27(3): 30503-030503.
[8]	牛春洋, 齐宏, 任亚涛, 阮立明. Apparent directional spectral emissivity determination of semitransparent materials[J]. 中国物理B, 2016, 25(4): 47801-047801.
[9]	乔要宾, 齐宏, 赵方舟, 阮立明. Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation[J]. 中国物理B, 2016, 25(12): 120201-120201.
[10]	舒剑. An efficient three-party password-based key agreement protocol using extended chaotic maps[J]. 中国物理B, 2015, 24(6): 60509-060509.
[11]	陈兴乐, 雷银照. Inverse problem of pulsed eddy current field of ferromagnetic plates[J]. , 2015, 24(3): 30301-030301.
[12]	谢琪, 胡斌, 陈克非, 刘文浩, 谭肖. Chaotic maps and biometrics-based anonymous three-party authenticated key exchange protocol without using passwords[J]. 中国物理B, 2015, 24(11): 110505-110505.
[13]	牛春洋, 齐宏, 黄兴, 阮立明, 王伟, 谈和平. Simultaneous reconstruction of temperature distribution and radiative properties in participating media using a hybrid LSQR–PSO algorithm[J]. 中国物理B, 2015, 24(11): 114401-114401.
[14]	胡淑娟, 邱春雨, 张利云, 黄启灿, 于海鹏, 丑纪范. An approach to estimating and extrapolating model error based on inverse problem methods：towards accurate numerical weather prediction[J]. , 2014, 23(8): 89201-089201.
[15]	朱俊杰, 蒋式勤, 王伟远, 赵晨, 吴燕华, 罗明, 权薇薇. Cardiac electrical activity imaging of patients with CRBBB or CLBBB in magnetocardiography[J]. 中国物理B, 2014, 23(4): 48702-048702.