Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh–Rose neuron model

doi:10.1088/1674-1056/23/3/030505

Abstract A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh–Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

Keywords: chaos neural firing bifurcation Hindmarsh–Rose model

Received: 22 June 2013
Revised: 30 August 2013
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	87.19.L-	(Neuroscience)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11072135).

Corresponding Authors: Jia Bing
E-mail: jiabing427@163.com;jiabing427@gmail.com

Cite this article:

Jia Bing (贾冰) Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh–Rose neuron model 2014 Chin. Phys. B 23 030505

[1]	Hindmarsh J L and Rose R M 1984 Proc. R Soc. London Ser. B 219 87
[2]	Holden A V and Fan Y S 1992 Chaos Soliton. Fract. 2 221
[3]	Fan Y S and Holden A V 1992 Chaos Soliton. Fract. 2 349
[4]	Fan Y S and Holden A V 1993 Chaos Soliton. Fract. 3 439
[5]	Wang X J 1993 Physica D 62 263
[6]	González-Miranda J M 2005 Phys. Rev. E 72 051922
[7]	González-Miranda J M 2003 Chaos 13 845
[8]	Innocenti G and Genesio R 2009 Chaos 19 023124
[9]	Braun H A, Wissing H and Schäfer K 1994 Nature 367 270
[10]	Sejnowski T J 1995 Nature 376 21
[11]	Yang M H, An S C, Gu H G, Liu Z Q and Ren W 2006 Neuro Report 17 995
[12]	Varela F, Lachaux J P, Rodriguez E and Martinerie J 2001 Nature Rev. Neurosci. 2 229
[13]	Dhamala M, Jirsa V K and Ding M 2004 Phys. Rev. Lett. 92 028101
[14]	Hansel D and Sompolinsky H 1992 Phys. Rev. Lett. 68 718
[15]	Dhamala M, Jirsa V K and Ding M 2004 Phys. Rev. Lett. 92 074104
[16]	Rosenblum M G and Pikovsky A S 2004 Phys. Rev. Lett. 92 114102
[17]	Jiang Y 2004 Phys. Rev. Lett. 93 229801
[18]	González-Miranda J M 2007 Int. J. Bifurc. Chaos Appl. Sci. Eng. 17 3071
[19]	Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G and Ren W 2009 Chin. Phys. Lett. 26 110501
[20]	Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G and Ren W 2010 Physica A 389 2642
[21]	Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G and Ren W 2009 Chin. Phys. Lett. 26 030504
[22]	Yuan L, Liu Z Q, Zhang H M, Yang M H, Wei C L, Ding X L, Gu H G and Ren W 2011 Chin. Phys. B 20 020508
[23]	Rech P C 2011 Phys. Lett. A 375 1461
[24]	Innocenti G, Morelli A, Genesio R and Torcini A 2007 Chaos 17 043128
[25]	Rech P C 2012 Chin. Phys. Lett. 29 060506
[26]	Linaro D, Poggi T and Storace M 2010 Phys. Lett. A 374 4589
[27]	Barrio R and Shilnikov A 2011 J. Math. Neurosci. 1 6
[28]	Shilnikov A L and Kolomiets M L 2008 Int. J. Bifurc. Chaos Appl. Sci. Eng. 18 2141
[29]	Linaro D, Champneys A, Desroches M and Storace M 2012 SIAM J. Appl. Dyn. Syst. 11 939
[30]	González-Miranda J M 2012 Chaos 22 013123
[31]	Gu H G, Jia B and Chen G R 2013 Phys. Lett. A 377 718
[32]	Wu X B, Mo J, Yang M H, Zheng Q H, Gu H G and Ren W 2008 Chin. Phys. Lett. 25 2799
[33]	Gu H G, Yang M H, Li L, Liu Z Q and Ren W 2003 Phys. Lett. A 319 89
[34]	Yang M H, Liu Z Q, Li L, Xu Y L, Liu H J, Gu H G and Ren W 2009 Int. J. Bifurc. Chaos Appl. Sci. Eng. 19 453
[35]	Gu H G, Yang M H, Li L, Liu Z Q and Ren W 2004 Dyn. Contin. Discr. Impul. Syst. Ser. B 11a 19
[36]	Gu H G, Yang M H, Li L, Liu Z Q and Ren W 2003 Int. J. Mod. Phys. B 17 4195
[37]	Gu H G, Yang M H, Li L, Liu Z Q and Ren W 2002 Neuro Report 13 1657
[38]	Mo J, Li Y Y, Wei C L, Yang M H, Liu Z Q, Gu H G, Qu S X and Ren W 2010 Chin. Phys. B 19 080513
[39]	Gu H G, Ren W, Lu Q S, Wu S G and Chen W J 2001 Phys. Lett. A 285 63
[40]	Wang D, Mo J, Zhao X Y, Gu H G, Qu S X and Ren W 2010 Chin. Phys. Lett. 27 070503
[41]	Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q and Ren W 2011 Int. J. Mod. Phys. B 25 3977
[42]	Gu H G 2013 Chaos 23 023126
[43]	Jia B, Gu H G, Li L and Zhao X Y 2012 Cogn. Neurodyn. 6 89
[44]	Bennett G J and Xie Y K 1988 Pain 33 87
[45]	Tal M and Eliav E 1996 Pain 64 511
[46]	Feudel U, Neiman A, Pei X, Wojtennek W, Braun H, Huber M and Moss F 2000 Chaos 10 231
[47]	Braun H A, Schäfer K, Voigt K, Peters R, Bretschneider F, Pei X, Wilkens L and Moss F 1997 J. Comput. Neurosci. 4 335
[48]	Braun H A, Schwabedal J, Dewald M, Finke C and Postnova S 2011 Chaos 21 047509
[49]	Kim M Y, Aguilar M, Hodge A, Vigmond E, Shrier A and Glass L 2009 Phys. Rev. Lett. 103 058101
[50]	Quail T, McVicar N, Aguilar M, Kim M Y, Hodge A, Glass L and Shrier A 2012 Chaos 22 033140
[51]	Farmer J D and Sidorowich J J 1987 Phys. Rev. Lett. 59 845
[52]	Theiler J, Eubank S, Longtin A, Galdrikian B and Farmer J D 1992 Physica D 58 77
[53]	Zheng Q H, Liu Z Q, Yang M H, Wu X B, Gu H G and Ren W 2009 Phys. Lett. A 373 540
[54]	Ma J, Ying H P, Liu Y and Li S R 2009 Chin. Phys. B 18 98
[55]	Wang C N, Ma J, Tang J and Li Y L 2010 Commun. Theor. Phys. 53 382
[56]	Schiff S J, Huang X and Wu J Y 2007 Phys. Rev. Lett. 98 178102
[57]	Huang X, Xu W, Liang J, Takagaki K, Gao X and Wu J Y 2010 Neuron 68 978

[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]	An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[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]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[5]	A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain Chunlei Fan(范春雷) and Qun Ding(丁群). Chin. Phys. B, 2023, 32(1): 010501.
[6]	Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[7]	Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Chin. Phys. B, 2022, 31(7): 074205.
[8]	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.
[9]	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.
[10]	Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[11]	Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
[12]	Energy spreading, equipartition, and chaos in lattices with non-central forces Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Chin. Phys. B, 2022, 31(2): 020506.
[13]	Resonance and antiresonance characteristics in linearly delayed Maryland model Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[14]	An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[15]	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.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh–Rose neuron model

Cite this article:

Online attention