Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(5): 050502    DOI: 10.1088/1674-1056/abcfa9
GENERAL Prev   Next  

Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns

Ben Cao(曹奔)1, Huaguang Gu(古华光)1,†, and Yuye Li(李玉叶)2,3
1 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
2 College of Mathematics and Computer Science, Chifeng University, Chifeng 024000, China;
3 Institute of Applied Mathematics, Chifeng University, Chifeng 024000, China
Abstract  In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be “Fold/Big Homoclinic” bursting and “Circle/Fold cycle” bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.
Keywords:  bifurcation      bursting      excitatory autapse      time delay  
Received:  05 October 2020      Revised:  30 October 2020      Accepted manuscript online:  02 December 2020
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  87.19.lg (Synapses: chemical and electrical (gap junctions))  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11872276 and 11762001) and the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region, China (Grant No. NJYT-20-A09).
Corresponding Authors:  Huaguang Gu     E-mail:

Cite this article: 

Ben Cao(曹奔), Huaguang Gu(古华光), and Yuye Li(李玉叶) Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns 2021 Chin. Phys. B 30 050502

[1] Glass L 2001 Nature 410 277
[2] Braun H A, Wissing H, Schäfer K and Hirsch M C 1994 Nature 367 270
[3] Yang Y, Cui Y H, Sang K N, Dong Y Y, NI Z Y, Ma S S and Hu H L 2018 Nature 554 317
[4] Mondal A, Upadhyay R K, Ma J, Yadav B K, Sharma S K and Mondal A 2019 Cogn. Neurodyn. 13 393
[5] Ma J, Yang Z Q, Yang L J and Tang J 2019 J. Zhejiang Univ. Sci. A 20 639
[6] Bacci A and Huguenard J R 2006 Neuron 49 119
[7] Yin L P, Zheng R, Ke W, He Q S, Zhang Y, Li J L, Wang B, Mi Z, Long Y S, Rasch M J, Li T F, Luan G M and Shu Y S 2018 Nat. Commun. 9 4890
[8] Kim S Y and Lim W 2020 Cogn. Neurodyn. 14 535
[9] Wu F Q, Gu H G and Li Y Y 2019 Commun. Nonlinear Sci. Numer. Simul. 79 104924
[10] Wu F Q and Gu H G 2020 Int. J. Bifur. Chaos 20 2030009
[11] Zhao Z G and Gu H G 2017 Sci. Rep. 7 7660
[12] Beiderbeck B, Myoga M H, Müller N, Callan A R, Friauf E, Grothe B and Pecka M 2018 Nat. Commun. 9 1771
[13] Dodla R and Rinzel J 2006 Phys. Rev. E 73 010903
[14] Goaillard J M, Taylor A L, Pulver S R and Marder E 2010 J. Neurosci. 30 4687
[15] Izhikevich E M 2000 Int. J. Bifurc. Chaos 10 1171
[16] Uzuntarla M, Torres J J, Calim A and Barreto E 2019 Neural Networks 110 131
[17] Franaszczuk P J, Kudela P and Bergey G K 2003 Epilepsy Res. 53 65
[18] Bacci A, Huguenard J R and Prince D A 2003 J. Neurosci. 23 859
[19] Saada R, Miller N, Hurwitz I and Susswein A J 2009 Curr. Biol. 19 479
[20] Ding X L, Jia B and Li Y Y 2019 Acta Phys. Sin. 68 180502 (in Chinese)
[21] Wang H T, Ma J, Chen Y L and Chen Y 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3242
[22] Guo D Q, Chen M M, Perc M, Wu S D, Xia C, Zhang Y S, Xu P, Xia Y and Yao D Z 2016 Europhys. Lett. 114 30001
[23] Song X L, Wang H T and Chen Y 2019 Nonlinear Dyn. 96 2341
[24] Uzun R 2017 Appl. Math. Comput. 315 203
[25] Song X L, Wang H T and Chen Y 2018 Nonlinear Dyn. 94 141
[26] Guo D Q, Wu S D, Chen M M, Perc M, Zhang Y S, Ma J L, Cui Y, Xu P, Xia Y and Yao D Z 2016 Sci. Rep. 6 26096
[27] Zhang X H and Liu S Q 2018 Chin. Phys. B 27 040501
[28] Yilmaz E, Ozer M, Baysal V and Perc M 2016 Sci. Rep. 6 30914
[29] Ge M Y, Xu Y, Zhang Z K, Peng Y X, Kang W J, Yang L J and Jia Y 2018 Eur. Phys. J. Spec. Top. 227 799
[30] Qin H X, Wu Y, Wang C N and Ma J 2015 Commun. Nonlinear Sci. Numer. Simul. 23 164
[31] Ma J, Song X L, Tang J and Wang C N 2015 Neurocomputing 167 378
[32] Yang X L, Yu Y H and Sun Z K 2017 Chaos 27 083117
[33] Wang Q Y, Murks A, Perc M and Lu Q S 2011 Chin. Phys. B 20 040504
[34] Tikidji-hamburyan R A, Martinez J J, White J A and Canavier C C 2015 J. Neurosci. 35 15682
[35] Zhao Z G, LI L, Gu H G and Gao Y 2020 Nonlinear Dyn. 99 1129
[36] Connelly W M 2014 PLoS ONE 9 e89995
[37] Deleuze C, Bhumbra G S, Pazienti A, Lourenco J, Mailhes C, Aguirre A, Beato M and Bacci A 2019 PLoS Biol. 17 e3000419
[38] Li Y Y, Gu H G and Ding X L 2019 Nonlinear Dyn. 97 2091
[39] Yao C G, He Z W, Nakano T, Qian Y and Shuai J W 2019 Nonlinear Dyn. 97 1425
[40] Zhao Z G, Li L and Gu H G 2020 Commun. Nonlinear Sci. Numer. Simul. 85 105250
[41] Cao B, Guan L N and Gu H G 2018 Acta Phys. Sin. 67 240502 (in Chinese)
[42] Wang X J 2010 Physiol. Rev. 90 1195
[43] Bekkers J M and Stevens C F 1991 Proc. Natl. Acad. Sci. USA 88 7834
[44] Pouzat C and Marty A 1998 J. Physiol-London 509 777
[45] Ermentrout B 2002 Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. (Philadelphia: SIAM)
[46] Ayata C and Lauritzen M 2015 Physiol. Rev. 95 953
[47] Ren G D, Zhou P, Ma J, Cai N, Alsaedi A and Ahmad B 2019 Int. J. Bifur. Chaos 27 1750187
[48] Zhang X J, Gu H G and Guan L N 2019 Sci. China Technol. Sci. 62 1502
[49] Guan L N, Gu H G and Jia Y B 2020 Nonlinear Dyn. 100 3645
[50] Wang Z L and Shi X R 2020 Cogn. Neurodyn. 14 115
[51] Xu Y, Liu M H, Zhu Z G and Ma J 2020 Chin. Phys. B 29 098704
[52] Jia B, Wu Y C, He D, Guo B H and Xue L 2018 Nonlinear Dyn. 93 1599
[53] Zhao Z G and Gu H G 2017 Procedia IUTAM 22 160
[54] Zhao Z G and Gu H G 2015 Chaos Soliton. Fract. 80 96
[1] Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays
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). Chin. Phys. B, 2023, 32(3): 038701.
[2] Effect of autaptic delay signal on spike-timing precision of single neuron
Xuan Ma(马璇), Yaya Zhao(赵鸭鸭), Yafeng Wang(王亚峰), Yueling Chen(陈月玲), and Hengtong Wang(王恒通). Chin. Phys. B, 2023, 32(3): 038703.
[3] Current bifurcation, reversals and multiple mobility transitions of dipole in alternating electric fields
Wei Du(杜威), Kao Jia(贾考), Zhi-Long Shi(施志龙), and Lin-Ru Nie(聂林如). Chin. Phys. B, 2023, 32(2): 020505.
[4] Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior
Xueyi Guan(管学义), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2022, 31(7): 070507.
[5] The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation and coexisting attractors
Yue Li(李月), Zengqiang Chen(陈增强), Mingfeng Yuan(袁明峰), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(6): 060503.
[6] Inferring interactions of time-delayed dynamic networks by random state variable resetting
Changbao Deng(邓长宝), Weinuo Jiang(蒋未诺), and Shihong Wang(王世红). Chin. Phys. B, 2022, 31(3): 030502.
[7] Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics
Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Chin. Phys. B, 2022, 31(3): 033101.
[8] Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation
Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[9] Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor
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). Chin. Phys. B, 2022, 31(10): 100503.
[10] Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay
Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Chin. Phys. B, 2022, 31(10): 100201.
[11] Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile
Xiao-Feng Shi(石晓峰), Dong-Jun Ma(马东军), Zong-Qiang Ma(马宗强), De-Jun Sun(孙德军), and Pei Wang(王裴). Chin. Phys. B, 2021, 30(9): 090201.
[12] Analysis and implementation of new fractional-order multi-scroll hidden attractors
Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立). Chin. Phys. B, 2021, 30(2): 020501.
[13] Stabilization strategy of a car-following model with multiple time delays of the drivers
Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2021, 30(12): 120506.
[14] Transition to chaos in lid-driven square cavity flow
Tao Wang(王涛) and Tiegang Liu(刘铁钢). Chin. Phys. B, 2021, 30(12): 120508.
[15] Enhance sensitivity to illumination and synchronization in light-dependent neurons
Ying Xie(谢盈), Zhao Yao(姚昭), Xikui Hu(胡锡奎), and Jun Ma(马军). Chin. Phys. B, 2021, 30(12): 120510.
No Suggested Reading articles found!