Abstract
On the basis of modified HR neuron model, this paper joins a depolarization direct current to investigate the dynamics of modified HR model under action of direct current with numerical computing method by adopting bifurcation diagram of inter-spike interval, the time responses diagram, the phase diagram and the two-parameter bifurcation diagram. These results indicate period adding bifurcation, period-doubling bifurcation as well as paroxysmal and intermittent chaos phenomenon in spiking neuron models can be observed clearly and intuitively, and not bifurcation structure of neuron model but ranges of parameters of various dynamic characteristics after adding direct current can be changed from the two-parameter bifurcation diagram.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aihara K, Matsumoto G (1986) Chaos, Manchester University Press. ENDEAVOUR. https://doi.org/10.1016/0160-9327(86)90107-9
Aihara K, Matsumoto G, Ichikawa M (1985) An alternating periodic-chaotic sequence observed in neural oscillators. Phys Rev Lett A 111:251–255. https://doi.org/10.1016/0375-9601(85)90256-7
Ananthkrishnan N, Sahai T (2001) Crisis critical junctures in the life of a chaotic attractor. Resonance 6:19–33. https://doi.org/10.1007/bf02837669
Bawin S, Sheppard A, Mahoney M, Adey W (1984) Influences of sinusoidal electric fields on excitability in the rat hippocampal slice. Brain Res Rev 323:227–237. https://doi.org/10.1016/0006-8993(84)90293-2
Bikson M, Inoue M, Akiyama H, Deans J, Fox J, Miyakawa H, Jefferys G (2004) Effects of uniform extracellular DC electric fields on excitability in rat hippocampal slices in vitro. J Physiol 557:175–190. https://doi.org/10.1113/jphysiol.2003.055772
Duan L, Lu Q, Cheng D (2009) Bursting of Morris-Lecar neuronal model with current-feedback control. Sci China Technol SC 52(3):771–781. https://doi.org/10.1007/s11431-009-0040-5
Eichwald C, Kaiser F (1995) Model for external influences on cellular signal transduction pathways including cytosolic calcium oscillations. Bioelectromagnetics 16:75–85. https://doi.org/10.1002/bem.2250160203
Enmentrout G (2004) High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J Comput Neurosci 16:211–235. https://doi.org/10.1023/b:jcns.0000025686.47117.67
Huang C, Xu B, Lin J (1999) Effects of extremely low frequency magnetic fields on hormone-induced cytosolic calcium oscillations. Acta Biochem Biophys Sin 15:543–546
Klimesch W, Sauseng P, Gerloff C (2003) Enhancing cognitive performance with repetitive transcranial magnetic stimulation at human individual alpha frequency. Eur J Neurosci 17:1129–1133. https://doi.org/10.1046/j.1460-9568.2003.02517.x
Lee S, Kim S (2006) Bifurcation analysis of mode-locking structure in a Hodgkin–Huxley neuron under sinusoidal current. Phys Rev E 73:041924. https://doi.org/10.1103/physreve.73.041924
Matsumoto G, Aihara K, Han Y, Akahashi N, Yoshizawa S, Nagumo J (1987) Chaos and phase locking in normal squid axons. Phys Lett A 123:162–166. https://doi.org/10.1016/0375-9601(87)90696-7
Ni H, Cho S, Mankoff J, Yang J, Dey AK (2018) Automated recognition of hypertension through overnight continuous hrv monitoring. J AMB INTEL HUM COMP 9(6):2011–2023. https://doi.org/10.1007/s12652-017-0471-y
Stuchly M, Dawson T (2000) Interaction of low-frequency electric and magnetic fields with the human body. Proc IEEE 88:643–664. https://doi.org/10.1109/5.849161
Tsaneva-Atanasova K, Osinga HM, Rieβ T, Sherman A (2010) Full system bifurcation analysis of endocrine bursting models. JMCB 264(4):1133–1146. https://doi.org/10.1016/j.jtbi.2010.03.030
Wang B, Xu W, Zhen C (2009) Fire patterns of coupled FitzHugh Nagumo neurons exposed to external electric field. Acta Phys Sin-Ch Ed 58(9):6590–6595
Wu K, Luo T, Lu H et al (2016) Bifurcation study of neuron firing activity of the modified Hindmarsh–Rose model. Neural Comput Appl 27(3):739–747. https://doi.org/10.1007/s00521-015-1892-1
Wu K, Zhang B, Tian B et al (2017) Synchronization study of Hindmarsh–Rose neuron coupled system based on numerical simulation of time delay. Cluster Comput 20(2):3287–3297. https://doi.org/10.1007/s10586-017-1063-5
Wu K, Wang D, Yu C et al (2018a) Synchronization of chemical synaptic coupling of the chay neuron system under time delay. Appl Sci-Basel 8(6):927–938
Wu K, Yu C, Wang D (2018b) The dynamics behaviors of chay neuron model under different parameters. Concurr Comp-Pract E. https://doi.org/10.1002/cpe.483
Wu K, Wang T, Wang C et al (2018c) Study on electrical synapse coupling synchronization of Hindmarsh-Rose neurons under Gaussian white noise. Neural Comput Appl 30(2):551–561. https://doi.org/10.1007/s00521-016-2681-1
Yang Z, Lu Q (2008) Different types of bursting in Chay neuronal model. Sci China Phys Mech 51(6):687–698
Yu H, Wang J, Deng B, Wei X (2010) Firing patterns of map-based neuron under extracellular alternating-current field. Acta Biochem Biophys Sin 26(10):907–918
Zhang X, Herzog H, Song J et al (2011) Response properties of the electrosensory neurons in hindbrain of the white sturgeon, Acipenser transmontanus. Neurosci Bull 27(6):422–429. https://doi.org/10.1007/s12264-011-1635-y
Acknowledgements
This work was supported by the Natural Science Fund Project of Gansu Province (No. 17JR5RA085) and Foundation of A Hundred Youth Talents Training Problem of Lanzhou Jiaotong University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wu, K., Li, W. & Wang, D. Bifurcation of modified HR neural model under direct current. J Ambient Intell Human Comput 11, 6211–6221 (2020). https://doi.org/10.1007/s12652-019-01478-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-019-01478-w