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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:  wch1227164@hnu.edu.cn

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)
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