Hölder continuity of generalized chaos synchronization in complex networks

doi:10.1088/1674-1056/20/9/090511

中国物理B ›› 2011, Vol. 20 ›› Issue (9): 90511-090511.doi: 10.1088/1674-1056/20/9/090511

Hölder continuity of generalized chaos synchronization in complex networks

胡爱花, 徐振源, 过榴晓

School of Science, Jiangnan University, Wuxi 214122, China

收稿日期:2011-02-16 修回日期:2011-04-17 出版日期:2011-09-15 发布日期:2011-09-15

Hölder continuity of generalized chaos synchronization in complex networks

Hu Ai-Hua(胡爱花)^†, Xu Zhen-Yuan(徐振源), and Guo Liu-Xiao(过榴晓)

School of Science, Jiangnan University, Wuxi 214122, China

Received:2011-02-16 Revised:2011-04-17 Online:2011-09-15 Published:2011-09-15

摘要/Abstract

摘要： A complex network consisting of chaotic systems is considered and the existence of the Hölder continuous generalized synchronization in the network is studied. First, we divide nodes of the network into two parts according to their dynamical behaviour. Then, based on the Schauder fixed point theorem, sufficient conditions for the existence of the generalized synchronization between them are derived. Moreover, the results are theoretically proved. Numerical simulations validate the theory.

关键词: generalized synchronization, H?, lder continuity, Schauder fixed point, chaotic system

Abstract: A complex network consisting of chaotic systems is considered and the existence of the Hölder continuous generalized synchronization in the network is studied. First, we divide nodes of the network into two parts according to their dynamical behaviour. Then, based on the Schauder fixed point theorem, sufficient conditions for the existence of the generalized synchronization between them are derived. Moreover, the results are theoretically proved. Numerical simulations validate the theory.

Key words: generalized synchronization, H?lder continuity, Schauder fixed point, chaotic system

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

胡爱花, 徐振源, 过榴晓. Hölder continuity of generalized chaos synchronization in complex networks[J]. 中国物理B, 2011, 20(9): 90511-090511.

Hu Ai-Hua(胡爱花), Xu Zhen-Yuan(徐振源), and Guo Liu-Xiao(过榴晓) . Hölder continuity of generalized chaos synchronization in complex networks[J]. Chin. Phys. B, 2011, 20(9): 90511-090511.

参考文献 32

[1]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Lu J Q and Cao J D 2007 Physica A 382 672
[3]	Hu M F and Xu Z Y 2008 Nonlinear Anal. Real World Appl. 9 1253
[4]	Zhou J, Xiang L and Liu Z R 2007 Physica A 384 684
[5]	Wu J S and Jiao L C 2008 Physica A 387 2111
[6]	Lu J Q and Cao J D 2007 Nonlinear Anal. Real World Appl. 8 1252
[7]	Li R H, Chen W S and Li S 2010 Chin. Phys. B 19 010508
[8]	Fu S H and Pei L J 2010 Acta Phys. Sin. 59 5985 (in Chinese)
[9]	Liu Y Z, Jiang C S and Lin C S 2007 Acta Phys. Sin. 56 707 (in Chinese)
[10]	Hu A H and Xu Z Y 2008 Phys. Lett. A 372 3814
[11]	González-Miranda J M 2002 Phys. Rev. E 65 047202
[12]	Uchida A, McAllister R, Meucci R and Roy R 2003 Phys. Rev. Lett. 91 174101
[13]	Rogers E, Kalra R, Schroll R, Uchida A, Lathrop D P and Roy R 2004 Phys. Rev. Lett. 93 084101
[14]	Li G H 2007 Chin. Phys. 16 2608
[15]	Rulkov N F, Sushchik M M and Tsimring L S 1995 Phys. Rev. E 51 980
[16]	Abarbanel H D I, Rulkov N F and Sushchik M M 1996 Phys. Rev. E 53 4528
[17]	Kocarev L and Parlitz U 1996 Phys. Rev. Lett. 76 1816
[18]	Hramov A E and Koronovskii A A 2005 Phys. Rev. E 71 067201
[19]	Li F, Hu A H and Xu Z Y 2006 Acta Phys. Sin. 55 590 (in Chinese)
[20]	Guo L X and Xu Z Y 2008 Acta Phys. Sin. 57 6086 (in Chinese)
[21]	Hu A H, Xu Z Y and Guo L X 2009 Acta Phys. Sin. 58 6030 (in Chinese)
[22]	Zhang R and Xu Z Y 2008 J. Sys. Sci. Math. Scis. 28 1509 (in Chinese)
[23]	Guo L X and Xu Z Y 2008 Chaos 18 033134
[24]	Hu A H, Xu Z Y and Guo L X 2009 Nonlinear Anal. Theory Methods Appl. 71 5994
[25]	Hu A H, Xu Z Y and Guo L X 2009 Phys. Lett. A 373 2319
[26]	Wu J S and Jiao L C 2008 Physica D 237 2487
[27]	Wu J S and Jiao L C 2008 IEEE Trans. Circ. Syst. II 55 932
[28]	Zhang Q L and Lü L 2011 Chin. Phys. B 20 010510
[29]	Qi W and Wang Y H 2009 Chin. Phys. B 18 1404
[30]	Hung Y C, Huang Y T, Ho M C and Hu C K 2008 Phys. Rev. E 77 016202
[31]	Wang R H and Wu Q Z 1979 Lectures on Ordinary Differential Equations (Beijing: Peopel Eduation Press) (in Chinese)
[32]	Ling Z S 1986 Almost Periodic Differential Equation and Integral Manifold (Shanghai: Shanghai Science and Technology Press) (in Chinese)

Hölder continuity of generalized chaos synchronization in complex networks

Hölder continuity of generalized chaos synchronization in complex networks

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Fangfang Zhang(张芳芳), Zhe Huang(黄哲), Lei Kou(寇磊), Yang Li(李扬), Maoyong Cao(曹茂永), and Fengying Ma(马凤英). Data encryption based on a 9D complex chaotic system with quaternion for smart grid[J]. 中国物理B, 2023, 32(1): 10502-010502.
[2]	Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Exponential sine chaotification model for enhancing chaos and its hardware implementation[J]. 中国物理B, 2022, 31(8): 80508-080508.
[3]	Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉). Solutions and memory effect of fractional-order chaotic system: A review[J]. 中国物理B, 2022, 31(6): 60501-060501.
[4]	Yue Li(李月), Zengqiang Chen(陈增强), Mingfeng Yuan(袁明峰), and Shijian Cang(仓诗建). The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation and coexisting attractors[J]. 中国物理B, 2022, 31(6): 60503-060503.
[5]	Peng-Fei Fang(方鹏飞), Han Liu(刘涵), Cheng-Mao Wu(吴成茂), and Min Liu(刘旻). Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model[J]. 中国物理B, 2022, 31(4): 40501-040501.
[6]	Jun Wang(王君), Yuan-Xi Zhang(张沅熙), Fan Wang(王凡), Ren-Jie Ni(倪仁杰), and Yu-Heng Hu(胡玉衡). Color-image encryption scheme based on channel fusion and spherical diffraction[J]. 中国物理B, 2022, 31(3): 34205-034205.
[7]	Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Explosive synchronization: From synthetic to real-world networks[J]. 中国物理B, 2022, 31(2): 20504-020504.
[8]	Fang-Fang Zhang(张芳芳), Rui Gao(高瑞), and Jian Liu(刘坚). Acoustic wireless communication based on parameter modulation and complex Lorenz chaotic systems with complex parameters and parametric attractors[J]. 中国物理B, 2021, 30(8): 80503-080503.
[9]	Tong-Feng Weng(翁同峰), Xin-Xin Cao(曹欣欣), and Hui-Jie Yang(杨会杰). Complex network perspective on modelling chaotic systems via machine learning[J]. 中国物理B, 2021, 30(6): 60506-060506.
[10]	Abdullah Zafar and Majid Khan. Energy behavior of Boris algorithm[J]. 中国物理B, 2021, 30(5): 55203-055203.
[11]	Fang Yuan(袁方), Cheng-Jun Bai(柏承君), and Yu-Xia Li(李玉霞). Cascade discrete memristive maps for enhancing chaos[J]. 中国物理B, 2021, 30(12): 120514-120514.
[12]	Chenguang Ma(马晨光), Santo Banerjee, Li Xiong(熊丽), Tianming Liu(刘天明), Xintong Han(韩昕彤), and Jun Mou(牟俊). Dynamical analysis, circuit realization, and application in pseudorandom number generators of a fractional-order laser chaotic system[J]. 中国物理B, 2021, 30(12): 120504-120504.
[13]	Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚). Adaptive synchronization of chaotic systems with less measurement and actuation[J]. 中国物理B, 2021, 30(10): 100503-100503.
[14]	Li-Lian Huang(黄丽莲), Shuai Liu(刘帅), Jian-Hong Xiang(项建弘), and Lin-Yu Wang(王霖郁). Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors[J]. 中国物理B, 2021, 30(10): 100506-100506.
[15]	郑俊, 胡汉平. A novel method of constructing high-dimensional digital chaotic systems on finite-state automata[J]. 中国物理B, 2020, 29(9): 90502-090502.