A new chaotic Hopfield network with piecewise linear activation function

doi:10.1088/1674-1056/19/3/030514

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30514-030514.doi: 10.1088/1674-1056/19/3/030514

A new chaotic Hopfield network with piecewise linear activation function

郑鹏升, 唐万生, 张建雄

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

收稿日期:2009-06-08 修回日期:2009-07-08 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
Project partially supported by the China Postdoctoral Science Foundation (Grant No.~20060400705) and Tianjin University Research Foundation (Grant No.~TJU-YFF-08B06).

A new chaotic Hopfield network with piecewise linear activation function

Zheng Peng-Sheng(郑鹏升), Tang Wan-Sheng(唐万生)^†, and Zhang Jian-Xiong(张建雄)

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

Received:2009-06-08 Revised:2009-07-08 Online:2010-03-15 Published:2010-03-15
Supported by:
Project partially supported by the China Postdoctoral Science Foundation (Grant No.~20060400705) and Tianjin University Research Foundation (Grant No.~TJU-YFF-08B06).

摘要/Abstract

摘要： This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.

Abstract: This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.

Key words: Hopfield network, chaos, piecewise linear function

中图分类号: (Numerical simulations of chaotic systems)

05.45.Pq

07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

郑鹏升, 唐万生, 张建雄. A new chaotic Hopfield network with piecewise linear activation function[J]. 中国物理B, 2010, 19(3): 30514-030514.

Zheng Peng-Sheng(郑鹏升), Tang Wan-Sheng(唐万生), and Zhang Jian-Xiong(张建雄). A new chaotic Hopfield network with piecewise linear activation function[J]. Chin. Phys. B, 2010, 19(3): 30514-030514.

参考文献 30

[1]	Guevara M R, Glass L, Mackey M C and Shrier A 1983 IEEE Trans. Syst. Man Cy. 13 790
[2]	Babloyantz A and Lourenco C 1996 Int. J. Neural Syst. 7 461
[3]	Freeman W J 1991 Sci. Am. 264 78
[4]	Yao Y and Freeman W J 1990 Neural Networks 3 153
[5]	Bersini H 1998 Neural Networks 11 1017
[6]	Bersini H and Sener P 2002 Neural Networks 15 1197
[7]	Li Q D, Yang X S and Yang F Y 2005 Neurocomputing 67 275
[8]	Huang Y and Yang X S 2006 Neurocomputing 69 1787
[9]	Wang S, Cai L, Kang Q, Wu G and Li Q 2008 Chin. Phys. B 17 2837
[10]	Yang X S and Yuan Q 2005 Neurocomputing 69 232
[11]	Yang X S and Huang Y 2006 Chaos 16 033114
[12]	Yang X S and Li Q D 2006 Int. J. Bifurcat. Chaos 16 157
[13]	Huang W Z and Huang Y 2008 Appl. Math. C 206 1
[14]	Zou F and Nossek J A 1993 IEEE Trans. Circuits Syst. 40 166
[15]	Yang X S and Huang Y 2007 Int. J. Bifurcat. Chaos 17 953
[16]	Yang X S and Li Q D 2007 Int. J. Bifurcat. Chaos 17 3211
[17]	Yang X S and Yuan Q 2008 Int. J. Bifurcat. Chaos 18 1337
[18]	Cao J and Lu J 2006 Chaos 16 013133
[19]	Cheng C, Liao T and Hwang C 2005 Chaos, Solitons and Fractals 24 197
[20]	Zhu W, Xu D and Huang Y 2008 Chaos, Solitons and Fractals 35 904
[21]	Wang M S, Hou Z H and Xin H W 2006 Chin. Phys. 15 2553
[22]	Wu W and Cui B T 2007 Chin. Phys. 16 1889
[23]	He G G, Zhu P, Chen H P and Cao Z T 2006 Acta Phys. Sin. 55 1040 (in Chinese)
[24]	Lou X Y and Cui B T 2008 Chin. Phys. B 17 520
[25]	Zhang Q 2008 Chin. Phys. B 17 125
[26]	Gao M and Cui B T 2009 Chin. Phys. B 18 76
[27]	Tan W, Wang Y, Zeng Z, Huang D and Zhou S 2004 Chin. Phys. 13 459
[28]	Qi W and Wang Y 2009 Chin. Phys. B 18 1404
[29]	Hopfield J J 1982 Proc. Natl. Acad. Sci. USA 79 2554
[30]	Hopfield J J 1984 Proc. Natl. Acad. Sci. USA 81 3088

Metrics

Viewed

Full text

HTML			PDF

最新录用	在线预览	正式出版	最新录用	在线预览	正式出版
0	0	0	0	0	98

来源	本网站	其他网站

次数	91	7
比例	93%	7%

Abstract

554

最新录用	在线预览	正式出版

0	0	554

	来源	本网站

	次数	554
	比例	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

A new chaotic Hopfield network with piecewise linear activation function

A new chaotic Hopfield network with piecewise linear activation function

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 30

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. 中国物理B, 2023, 32(3): 30203-030203.
[2]	Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays[J]. 中国物理B, 2023, 32(3): 38701-038701.
[3]	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.
[4]	Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成). Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse[J]. 中国物理B, 2023, 32(1): 10503-010503.
[5]	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.
[6]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Wei-Peng Lyu(吕伟鹏), and Qin-Sheng Bi(毕勤胜). Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor[J]. 中国物理B, 2022, 31(10): 100503-100503.
[7]	Zhi-Wei Jia(贾志伟), Li Li(李丽), Yi-Yan Guo(郭一岩), An-Bang Wang(王安帮), Hong Han(韩红), Jin-Chuan Zhang(张锦川), Pu Li(李璞), Shen-Qiang Zhai(翟慎强), and Feng-Qi Liu(刘峰奇). Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers[J]. 中国物理B, 2022, 31(10): 100505-100505.
[8]	Xian-Jia Wang(王先甲) and Lin-Lin Wang(王琳琳). Evolution of donations on scale-free networks during a COVID-19 breakout[J]. 中国物理B, 2022, 31(8): 80204-080204.
[9]	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.
[10]	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.
[11]	Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). The dynamics of a memristor-based Rulkov neuron with fractional-order difference[J]. 中国物理B, 2022, 31(6): 60502-060502.
[12]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超),Hai-Bo Jiang(姜海波), and Qin-Sheng Bi(毕勤胜). A class of two-dimensional rational maps with self-excited and hidden attractors[J]. 中国物理B, 2022, 31(3): 30503-030503.
[13]	Fei Yu(余飞), Zinan Zhang(张梓楠), Hui Shen(沈辉), Yuanyuan Huang(黄园媛), Shuo Cai(蔡烁), and Sichun Du(杜四春). FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient[J]. 中国物理B, 2022, 31(2): 20505-020505.
[14]	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.
[15]	Tao Wang(王涛) and Tiegang Liu(刘铁钢). Transition to chaos in lid-driven square cavity flow[J]. 中国物理B, 2021, 30(12): 120508-120508.