Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(6): 060502    DOI: 10.1088/1674-1056/ac539a
Special Issue: SPECIAL TOPIC— Interdisciplinary physics: Complex network dynamics and emerging technologies
SPECIAL TOPIC—Interdisciplinary physics: Complex network dynamics and emerging technologies Prev   Next  

The dynamics of a memristor-based Rulkov neuron with fractional-order difference

Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪)
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Abstract  The exploration of the memristor model in the discrete domain is a fascinating hotspot. The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors. However, most of the current investigations are based on the integer-order discrete memristor, and there are relatively few studies on the form of fractional order. In this paper, a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator. Furthermore, the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor. The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph, the Lyapunov exponential spectrum, and the iterative graph. The results demonstrate that the fractional-order system has more abundant dynamics than the integer one, such as hyper-chaos, multi-stable and transient chaos. In addition, the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system. The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future.
Keywords:  discrete memristor      Rulkov neuron      fractional-order difference      dynamics  
Received:  07 December 2021      Revised:  21 January 2022      Accepted manuscript online:  10 February 2022
PACS:  05.45.Ac (Low-dimensional chaos)  
  05.45.-a (Nonlinear dynamics and chaos)  
  87.19.ll (Models of single neurons and networks)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91964108), the National Natural Science Foundation of China (Grant No. 61971185), and the Natural Science Foundation of Hunan Province, China (Grant No. 2020JJ4218).
Corresponding Authors:  Chun-Hua Wang     E-mail:

Cite this article: 

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 2022 Chin. Phys. B 31 060502

[1] Lin H R and Wang C H 2020 Appl. Math. Comput. 369 124840
[2] LV M and Ma J 2016 Neurocomputing 205 375
[3] Lin H R, Wang C H, Hong Q H and Sun Y C 2020 IEEE Transactions on Circuits and Systems II: Express Briefs 67 3472
[4] Lin H R, Wang C H, Chen C J, Sun Y C, Xu C and Hong Q H 2021 IEEE Transactions on Circuits and Systems I: Regular Papers 68 3397
[5] Hodgkin A L and Huxley A F 1990 Bull. Math. Bio. 52 25
[6] Hindmarsh J and Rose R M 1984 Proceedings of the Royal Society of London. Series B, Biological Sciences 221 87
[7] Izhikevich and E M 2003 IEEE Trans. Neural Networks 14 1569
[8] Rulkov N F 2001 Phys. Rev. Lett. 86 183
[9] Bao H, Hua Z Y, Li H Z, Chen M and Bao B C 2021 IEEE Transactions on Circuits and Systems I: Regular Papers 68 4534
[10] Li K X, Bao H, Li H Z, Ma J, Hua Z Y and Bao B C 2021 IEEE Transactions on Industrial Informatics PP 1
[11] Hilfer R 2000 World Scientific Computer Sci. 463 472
[12] Petras I 2010 IEEE Transactions on Circuits and Systems II-Express Briefs 57 975
[13] Ahmad W M and Sprott J C 2003 Chaos, Solitons & Fractals 16 339
[14] Lu J G and Chen G R 2006 Chaos, Solitons & Fractals 27 685
[15] Dong J, Zhang G J, Xie Y, Yao H and Wang J 2014 Cognitive Neurodynamics 8 167
[16] Wei Y H 2021 Nonlinear Dynamics 104 3643
[17] Yang N N, Han Y C, Wu C J, Jia R and Liu C X 2017 Chin. Phys. B 26 080503
[18] Xie W L, Wang C H and Lin H R 2021 Nonlinear Dynamics 104 4523
[19] Li R G and Wu H N 2019 Nonlinear Dynamics 95 1221
[20] Miller K S and Ross B 1989 Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications 139-152
[21] Edelman M 2012 Discontinuity, Nonlinearity and Complexity 1 305
[22] Edelman M 2015 Discontinuity, Nonlinearity and Complexity 4 391
[23] Khennaoui A A, Quannas A, Bendoukha S, Wang X and Pham V T 2018 Entropy 20 530
[24] Liu Z Y, Xia T C and Wang J B 2018 Chin. Phys. B 27 030502
[25] Peng Y X, Sun K H, He S B and Peng D 2019 Entropy 21 27
[26] Chua L 1971 IEEE Trans. Circuit Theory 18 507
[27] Strukov D B, Snider G S, Stewart D R and Williams R S 2008 Nature 453 80
[28] Yang Z L, Liang D, Ding D W, Hu Y B and Li H 2021 Chin. Phys. B 30 120515
[29] Zhou L, Wang C H and Zhou L L 2018 International Journal of Circuit Theory and Applications 46 84
[30] Guo M, Liu R Y, Dou M L and Dou G 2021 Chin. Phys. B 30 068402
[31] Yang L M and Wang C H 2021 Neurocomputing 460 117
[32] Cheng G F, Wang C H and Xu C 2020 Multimedia Tools and Applications 79 29243
[33] Chai X L, Gan Z H, Lu Y, Zhang M H and Chen Y R 2016 Chin. Phys. B 25 100503
[34] Coopmans C, Pet I and Chen Y Q 2009 ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, August 2, 2009, San Diego, USA
[35] Peng Y X, He S B and Sun K H 2021 Results in Physics 24 104106
[36] Abdeljawad T 2011 Comput. Math. Appl. 62 1602
[37] Nosrati K and Shafiee M 2018 Chaos, Solitons & Fractals 115 224
[38] Ji Y D, Lai L and Zhou S C 2017 Commun. Nonlinear Sci. Numer. Simul. 57 352
[39] Atici F and Eloe P W 2009 Proc. Am. Math. Soc. 137 981
[40] Bao H, Hu A H, Liu W B and Bao B C 2019 IEEE Transactions on Neural Net-works and Learning Systems 31 502
[41] Li H Z, Hua Z Y, Bao H, Zhu L, Chen M and Bao B C 2021 IEEE Transactions on Industrial Electronics 68 9931
[42] Adhikari S P, Sah M, Kim H and Chua L 2013 IEEE Transactions on Circuits & Systems. Part I: Regular Papers 60 3008
[43] Rajasekar S, Used J and Wagemakers A 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3435
[44] Wang, C X and Cao H J 2014 Commun. Nonlinear Sci. Numer. Simul. 20 536
[45] Irina Bashkirtseva 2015 Discrete Dynamics in Nature & Society 2015 1
[46] Yu S M 2011 Chaotic systems and chaotic circuits:principle, design and its appliction in communications (Xi'an: Xidian University Press) pp. 10-58
[47] Eva K and Seenith S 2012 Nonlinear Analysis: Real World Applications 13 1489
[48] Kang Y M, Xie Y, Lu J C and Jiang J 2015 Nonlinear Dynamics 82 1259
[49] Danca M F, Feckan M, Kuznetsov N V and Chen G R 2018 Nonlinear Dynamics 91 2523
[50] Wu G C and Baleanu D 2015 Commun. Nonlinear Sci. Numeri. Simul. 22 95
[51] Wolf A, Swift J, Harry L S and Vastano J 1985 Physica D 16 285
[52] Ouannas A, Khennaoui A A, Wang X, Pham V T, Boulaaras S and Momani S 2020 The European Physical Journal Special Topics 229 2261
[53] Yu F, Qian S, Chen X, Huang Y Y, Liu L, Shi C Q, Cai S, Song Y and Wang C H 2020 Int. J. Bifurc. Chaos 30 2050147
[54] Lin H R, Wang C H, Deng Q L, Xu C, Deng Z K and Zhou C 2021 Nonlinear Dynamics 106 959
[55] Celso G, Edward O and James A Y 1986 Phys. Rev. Lett. 57 1284
[56] Sun K H, He S B, He Y and Yin L Z 2013 Acta Phys. Sin. 62 010501 (in Chinese)
[1] Cascade excitation of vortex motion and reentrant superconductivity in flexible Nb thin films
Liping Zhang(张丽萍), Zuyu Xu(徐祖雨), Xiaojie Li(黎晓杰), Xu Zhang(张旭), Mingyang Qin(秦明阳), Ruozhou Zhang(张若舟), Juan Xu(徐娟), Wenxin Cheng(程文欣), Jie Yuan(袁洁), Huabing Wang(王华兵), Alejandro V. Silhanek, Beiyi Zhu(朱北沂), Jun Miao(苗君), and Kui Jin(金魁). Chin. Phys. B, 2023, 32(4): 047302.
[2] Conductive path and local oxygen-vacancy dynamics: Case study of crosshatched oxides
Z W Liang(梁正伟), P Wu(吴平), L C Wang(王利晨), B G Shen(沈保根), and Zhi-Hong Wang(王志宏). Chin. Phys. B, 2023, 32(4): 047303.
[3] Heterogeneous hydration patterns of G-quadruplex DNA
Cong-Min Ji(祭聪敏), Yusong Tu(涂育松), and Yuan-Yan Wu(吴园燕). Chin. Phys. B, 2023, 32(2): 028702.
[4] Molecular dynamics study of interactions between edge dislocation and irradiation-induced defects in Fe–10Ni–20Cr alloy
Tao-Wen Xiong(熊涛文), Xiao-Ping Chen(陈小平), Ye-Ping Lin(林也平), Xin-Fu He(贺新福), Wen Yang(杨文), Wang-Yu Hu(胡望宇), Fei Gao(高飞), and Hui-Qiu Deng(邓辉球). Chin. Phys. B, 2023, 32(2): 020206.
[5] Realization of the iSWAP-like gate among the superconducting qutrits
Peng Xu(许鹏), Ran Zhang(张然), and Sheng-Mei Zhao(赵生妹). Chin. Phys. B, 2023, 32(2): 020306.
[6] Formation of nanobubbles generated by hydrate decomposition: A molecular dynamics study
Zilin Wang(王梓霖), Liang Yang(杨亮), Changsheng Liu(刘长生), and Shiwei Lin(林仕伟). Chin. Phys. B, 2023, 32(2): 023101.
[7] Effects of adjacent bubble on spatiotemporal evolutions of mechanical stresses surrounding bubbles oscillating in tissues
Qing-Qin Zou(邹青钦), Shuang Lei(雷双), Zhang-Yong Li(李章勇), and Dui Qin(秦对). Chin. Phys. B, 2023, 32(1): 014302.
[8] Linear analysis of plasma pressure-driven mode in reversed shear cylindrical tokamak plasmas
Ding-Zong Zhang(张定宗), Xu-Ming Feng(冯旭铭), Jun Ma(马骏), Wen-Feng Guo(郭文峰), Yan-Qing Huang(黄艳清), and Hong-Bo Liu(刘洪波). Chin. Phys. B, 2023, 32(1): 015201.
[9] Prediction of flexoelectricity in BaTiO3 using molecular dynamics simulations
Long Zhou(周龙), Xu-Long Zhang(张旭龙), Yu-Ying Cao(曹玉莹), Fu Zheng(郑富), Hua Gao(高华), Hong-Fei Liu(刘红飞), and Zhi Ma(马治). Chin. Phys. B, 2023, 32(1): 017701.
[10] Adsorption dynamics of double-stranded DNA on a graphene oxide surface with both large unoxidized and oxidized regions
Mengjiao Wu(吴梦娇), Huishu Ma(马慧姝), Haiping Fang(方海平), Li Yang(阳丽), and Xiaoling Lei(雷晓玲). Chin. Phys. B, 2023, 32(1): 018701.
[11] Finite superconducting square wire-network based on two-dimensional crystalline Mo2C
Zhen Liu(刘震), Zi-Xuan Yang(杨子萱), Chuan Xu(徐川), Jia-Ji Zhao(赵嘉佶), Lu-Junyu Wang(王陆君瑜), Yun-Qi Fu(富云齐), Xue-Lei Liang(梁学磊), Hui-Ming Cheng(成会明), Wen-Cai Ren(任文才), Xiao-Song Wu(吴孝松), and Ning Kang(康宁). Chin. Phys. B, 2022, 31(9): 097404.
[12] State-to-state integral cross sections and rate constants for the N+(3P)+HD→NH+/ND++D/H reaction: Accurate quantum dynamics studies
Hanghang Chen(陈航航), Zijiang Yang(杨紫江), and Maodu Chen(陈茂笃). Chin. Phys. B, 2022, 31(9): 098204.
[13] Atomic structure and collision dynamics with highly charged ions
Xinwen Ma(马新文), Shaofeng Zhang(张少锋), Weiqiang Wen(汶伟强), Zhongkui Huang(黄忠魁), Zhimin Hu(胡智民), Dalong Guo(郭大龙), Junwen Gao(高俊文), Bennaceur Najjari, Shenyue Xu(许慎跃), Shuncheng Yan(闫顺成), Ke Yao(姚科), Ruitian Zhang(张瑞田), Yong Gao(高永), and Xiaolong Zhu(朱小龙). Chin. Phys. B, 2022, 31(9): 093401.
[14] Probing subcycle spectral structures and dynamics of high-order harmonic generation in crystals
Long Lin(林龙), Tong-Gang Jia(贾铜钢), Zhi-Bin Wang(王志斌), and Peng-Cheng Li(李鹏程). Chin. Phys. B, 2022, 31(9): 093202.
[15] Effect of spatial heterogeneity on level of rejuvenation in Ni80P20 metallic glass
Tzu-Chia Chen, Mahyuddin KM Nasution, Abdullah Hasan Jabbar, Sarah Jawad Shoja, Waluyo Adi Siswanto, Sigiet Haryo Pranoto, Dmitry Bokov, Rustem Magizov, Yasser Fakri Mustafa, A. Surendar, Rustem Zalilov, Alexandr Sviderskiy, Alla Vorobeva, Dmitry Vorobyev, and Ahmed Alkhayyat. Chin. Phys. B, 2022, 31(9): 096401.
No Suggested Reading articles found!