Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model

doi:10.1088/1674-1056/24/3/030503

›› 2015, Vol. 24 ›› Issue (3): 30503-030503.doi: 10.1088/1674-1056/24/3/030503

Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model

罗润梓, 张春华

Department of Mathematics, Nanchang University, Nanchang 330031, China

收稿日期:2014-06-29 修回日期:2014-09-15 出版日期:2015-03-05 发布日期:2015-03-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11361043 and 61304161), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20122BAB201005), and the Scientific and Technological Project Foundation of Jiangxi Province Education Office, China (Grant No. GJJ14156).

Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model

Luo Run-Zi (罗润梓), Zhang Chun-Hua (张春华)

Department of Mathematics, Nanchang University, Nanchang 330031, China

Received:2014-06-29 Revised:2014-09-15 Online:2015-03-05 Published:2015-03-05
Contact: Luo Run-Zi E-mail:luo_rz@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11361043 and 61304161), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20122BAB201005), and the Scientific and Technological Project Foundation of Jiangxi Province Education Office, China (Grant No. GJJ14156).

摘要/Abstract

摘要： This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh-Rose (HR) neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.

关键词: chaotic system, state observer, scalar input

Abstract: This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh-Rose (HR) neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.

Key words: chaotic system, state observer, scalar input

中图分类号: (Control of chaos, applications of chaos)

05.45.Gg

罗润梓, 张春华. Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model[J]. , 2015, 24(3): 30503-030503.

Luo Run-Zi (罗润梓), Zhang Chun-Hua (张春华). Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model[J]. Chin. Phys. B, 2015, 24(3): 30503-030503.

参考文献 22

[1]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Kwon O M, Son J W and Lee S M 2013 Nonlinear Dyn. 72 129
[3]	Luo R Z, Wang Y L and Deng S C 2011 Chaos 21 043114
[4]	Yang D D 2014 Chin. Phys. B 23 010504
[5]	Luo R Z and Wang Y L 2014 Indian J. Phys. 88 301
[6]	Li G H, Zhou S P and Xu D M 2004 Chin. Phys. 13 168
[7]	Starkov K E, Coria L N and Aguilar L T 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 17
[8]	Kuntanapreeda S 2012 Computers and Mathematics with Applications 63 183
[9]	Yang J Q and Zhu F L 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 926
[10]	Shi H J, Sun Y Z and Zhao D H 2014 Nonlinear Dyn. 75 817
[11]	Wu R C and Cao D X 2013 PRAMANA-Journal of Phys. 81 727
[12]	Gao Y B, Sun B H and Lu G P 2013 Appl. Math. Model. 37 4993
[13]	Mahmoud E E 2013 Math. Comput. Simul. 89 69
[14]	Shi Y C, Zhu P Y and Qin K 2014 Neurocomputing 123 443
[15]	Chen S H, Wang F and Wang C P 2004 Chaos Soliton. Fract. 20 235
[16]	Wang G M 2010 Phys. Lett. A 374 2831
[17]	Zhen R, Liu J, Wu X, Wu X, Zhu Q, Wang Y and Nouri H 2013 Int. J. Modelling, Identification and Control 20 164
[18]	Zhang R X and Yang S P 2012 Chin. Phys. B 21 080505
[19]	Lu J Q, Hoc D W C, Cao J D and Kurths J 2013 Nonlinear Analysis: Real World Applications 14 581
[20]	Luo R Z and He L M 2014 Chin. Phys. B 23 070506
[21]	Rössler O E 1976 Phys. Lett. 57 397
[22]	Hindmarsh J L and Rose R M 1984 Proc. R. Soc. London, Ser. B 221 87

Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model

Observer of a class of chaotic systems: An application to Hindmarsh-Rose neuronal model

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 22

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]	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.
[4]	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.
[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]	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.
[12]	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.
[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.