Journal of Zhejiang University-SCIENCE A

, Volume 20, Issue 9, pp 639–659 | Cite as

A physical view of computational neurodynamics

  • Jun MaEmail author
  • Zhuo-qin Yang
  • Li-jian Yang
  • Jun Tang


The nervous system is made of a large number of neurons. Time-varying balance between excitatory and inhibitory neurons is important to activate appropriate modes of electrical activity. A realistic biological neuron is complex, often presenting various electrophysiological activities and diffusive propagation of ions in the cell. Therefore, the physical effects of electromagnetic induction become very important and should be considered when estimating signal encoding and mode selection. Synaptic plasticity and anatomical structure have been developed to enhance the self-adaption of neurons. Thus, the electrical mode with the most effective links and weights can be selected to benefit information encoding and signal propagation between neurons in the network. As a result, the demand for metabolic energy can be greatly reduced. In this review, neuron model setting with biophysical effects, modulation of astrocytes, autapse formation and biological function, synaptic plasticity, memristive synapses, and field coupling between neurons and networks are reviewed briefly to provide guidance in the field of neurodynamics.

Key words

Neuron Neural networks Autapse Hamilton energy Electromagnetic induction 



目 的

基于物理学基本原理解释神经元电活动过程中存 在的物理效应,解释突触生物功能活化过程的物 理机制,以及分析神经元建模中的电磁场效应 (图1)。探讨神经元建模、胶质细胞调控、突触 可塑性和神经元群体电活动的网络效应。


1. 论证荷控和磁控忆阻器非线性函数在物理神经 元模型构建中的作用。 2. 提出神经元突触耦合的 物理机制就是电场和磁场耦合(图3)。 3. 研究神 经元电路混合突触耦合的物理实现(图2)以及 能量存储与泵浦。

方 法

依据物理学电磁感应定律和赫姆霍兹定理论证神 经元电活动过程产生的电磁感应效应以及能量 输运过程。基于忆阻器物理特性和量纲一致原理 来构建物理神经元模型,从物理角度解释突触功 能实现过程的物理机制。

结 论

在神经元电活动过程中需考虑电磁感应效应;场 耦合可以调控神经元突触耦合作用;在神经元网 络中信号传递需考虑物理场耦合过程。


神经元 神经网络 自突触 哈密顿能量 电磁感应 

CLC number

O59 TN710 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. Abbott LF, Nelson SB, 2000. Synaptic plasticity: taming the beast. Nature Neuroscience, 3(11):1178–1183. CrossRefGoogle Scholar
  2. Abraham WC, Bear MF, 1996. Metaplasticity: the plasticity of synaptic plasticity. Trends in Neurosciences, 19(4):126–130. CrossRefGoogle Scholar
  3. Ajay SM, Bhalla US, 2004. A role for ERKII in synaptic pattern selectivity on the time-scale of minutes. European Journal of Neuroscience, 20(10):2671–2680. CrossRefGoogle Scholar
  4. Ajay SM, Bhalla US, 2007. A propagating ERKII switch forms zones of elevated dendritic activation correlated with plasticity. HFSP Journal, 1(1):49–66. CrossRefGoogle Scholar
  5. Allegrini P, Fronzoni L, Pirino D, 2009. The influence of the astrocyte field on neuronal dynamics and synchronization. Journal of Biological Physics, 35(4):413–423. CrossRefGoogle Scholar
  6. Amiri M, Bahrami F, Janahmadi M, 2012. Functional contributions of astrocytes in synchronization of a neuronal network model. Journal of Theoretical Biology, 292:60-0.
  7. Amiri M, Bahrami F, Janahmadi M, 2012. Modified thalamocortical model: a step towards more understanding of the functional contribution of astrocytes to epilepsy. Journal of Computational Neuroscience, 33(2):285–299. MathSciNetCrossRefGoogle Scholar
  8. Amiri M, Bahrami F, Janahmadi M, 2012. On the role of astrocytes in epilepsy: a functional modeling approach. Neuroscience Research, 72(2):172–180. zbMATHCrossRefGoogle Scholar
  9. Amiri M, Hosseinmardi N, Bahrami F, et al., 2013. Astrocyteneuron interaction as a mechanism responsible for generation of neural synchrony: a study based on modeling and experiments. Journal of Computational Neuroscience, 34(3):489–504. MathSciNetCrossRefGoogle Scholar
  10. Araque A, Carmignoto G, Haydon PG, et al., 2014. Gliotransmitters travel in time and space. Neuron, 81(4): 728–739.
  11. Azghadi MR, Linares- Barranco B, Abbott D, et al., 2017. A hybrid CMOS-memristor neuromorphic synapse. IEEE Transactions on Biomedical Circuits and Systems, 11(2): 434–445. CrossRefGoogle Scholar
  12. Bao H, Liu WB, Chen M, 2019. Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh–Nagumo circuit. Nonlinear Dynamics, 96(3):1879–1894. CrossRefGoogle Scholar
  13. Bear MF, Malenka RC, 1994. Synaptic plasticity: LTP and LTD. Current Opinion in Neurobiology, 4(3):389–399. CrossRefGoogle Scholar
  14. Bennett MR, Farnell L, Gibson WG, 2008. Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells. Journal of Theoretical Biology, 250(1):172–185. MathSciNetzbMATHCrossRefGoogle Scholar
  15. Bezprozvanny I, Watras J, Ehrlich BE, 1991. Bell-shaped calcium-response curves of Ins(1,4,5)P3- and calciumgated channels from endoplasmic reticulum of cerebellum. Nature, 351(6329):751–754. CrossRefGoogle Scholar
  16. Bhalla US, 2002. Mechanisms for temporal tuning and filtering by postsynaptic signaling pathways. Biophysical Journal, 83(2):740–752. CrossRefGoogle Scholar
  17. Bhalla US, 2004. Signaling in small subcellular volumes. II. Stochastic and diffusion effects on synaptic network properties. Biophysical Journal, 87(2):745–753. CrossRefGoogle Scholar
  18. Bhalla US, Iyengar R, 1999. Emergent properties of networks of biological signaling pathways. Science, 283(5400): 381–387. CrossRefGoogle Scholar
  19. Blackwell KT, Jedrzejewska-Szmek J, 2013. Molecular mechanisms underlying neuronal synaptic plasticity: systems biology meets computational neuroscience in the wilds of synaptic plasticity. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 5(6):717–731. Google Scholar
  20. Bliss TVP, Lømo T, 1973. Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. The Journal of Physiology, 232(2):331–356. CrossRefGoogle Scholar
  21. Bliss TVP, Gardner- Medwin AR, 1973. Long-lasting potentiation of synaptic transmission in the dentate area of the unanaesthetized rabbit following stimulation of the perforant path. The Journal of Physiology, 232(2):357–374. CrossRefGoogle Scholar
  22. Bliss TVP, Collingridge GL, 1993. A synaptic model of memory: long-term potentiation in the hippocampus. Nature, 361(6407):31–39. Google Scholar
  23. Bui L, Glavinović MI, 2013. Synaptic activity slows vesicular replenishment at excitatory synapses of rat hippocampus. Cognitive Neurodynamics, 7(2):105–120. CrossRefGoogle Scholar
  24. Buonomano DV, 2000. Decoding temporal information: a model based on short-term synaptic plasticity. Journal of Neuroscience, 20(3):1129–1141. CrossRefGoogle Scholar
  25. Busciglio J, Lorenzo A, Yankner BA, 1992. Methodological variables in the assessment of beta amyloid neurotoxicity. Neurobiology of Aging, 13(5):609–612. CrossRefGoogle Scholar
  26. Carro-Pérez I, Sánchez-López C, González-Hernández HG, 2018. Experimental verification of a memristive neural network. Nonlinear Dynamics, 93(4):1823–1840. CrossRefGoogle Scholar
  27. Chan SC, Mok SY, Ng DWK, et al., 2017. The role of neuron–glia interactions in the emergence of ultra-slow oscillations. Biological Cybernetics, 111(5–6):459–472. MathSciNetzbMATHCrossRefGoogle Scholar
  28. Chander BS, Chakravarthy VS, 2012. A computational model of neuro-glio-vascular loop interactions. PLoS One, 7(11):e48802. CrossRefGoogle Scholar
  29. Coba MP, Pocklington AJ, Collins MO, et al., 2009. Neurotransmitters drive combinatorial multistate postsynaptic density networks. Science Signaling, 2(68):ra19. CrossRefGoogle Scholar
  30. Collins MO, Yu L, Coba MP, et al., 2005. Proteomic analysis of in vivo phosphorylated synaptic proteins. The Journal of Biological Chemistry, 280(7):5972–5982. CrossRefGoogle Scholar
  31. Covi E, Brivio S, Serb A, et al., 2016. Analog memristive synapse in spiking networks implementing unsupervised learning. Frontiers in Neuroscience, 10:482. CrossRefGoogle Scholar
  32. Dani JW, Chernjavsky A, Smith SJ, 1992. Neuronal activity triggers calcium waves in hippocampal astrocyte networks. Neuron, 8(3):429–440. CrossRefGoogle Scholar
  33. de Pittà M, Volman V, Berry H, et al., 2012. Computational quest for understanding the role of astrocyte signaling in synaptic transmission and plasticity. Frontiers in Computational Neuroscience, 6:98. CrossRefGoogle Scholar
  34. de Young GW, Keizer J, 1992. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agoniststimulated oscillations in Ca2+ concentration. Proceedings of the National Academy of Sciences of the United States of America, 89(20):9895–9899. CrossRefGoogle Scholar
  35. Engert F, Bonhoeffer T, 1999. Dendritic spine changes associated with hippocampal long-term synaptic plasticity. Nature, 399(6731):66–70. CrossRefGoogle Scholar
  36. Fitzhugh R, 1966. Theoretical effect of temperature on threshold in the Hodgkin-Huxley nerve model. The Journal of General Physiology, 49(5):989–1005. CrossRefGoogle Scholar
  37. Gamble E, Koch C, 1987. The dynamics of free calcium in dendritic spines in response to repetitive synaptic input. Science, 236(4806):1311–1315. CrossRefGoogle Scholar
  38. Ge MY, Xu Y, Zhang ZK, et al., 2018. Autaptic modulationinduced neuronal electrical activities and wave propagation on network under electromagnetic induction. The European Physical Journal Special Topics, 227(7–9):799–809. CrossRefGoogle Scholar
  39. Ge MY, Jia Y, Xu Y, et al., 2018. Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dynamics, 91(1):515–523. CrossRefGoogle Scholar
  40. Giaume C, Koulakoff A, Roux L, et al., 2010. Astroglial networks: a step further in neuroglial and gliovascular interactions. Nature Reviews Neuroscience, 11(2):87–99. CrossRefGoogle Scholar
  41. Gibson WG, Farnell L, Bennett MR, 2007. A computational model relating changes in cerebral blood volume to synaptic activity in neurons. Neurocomputing, 70(10–12): 1674–1679. CrossRefGoogle Scholar
  42. Goldwyn JH, Imennov NS, Famulare M, et al., 2011. Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons. Physical Review E, 83(4): 041908. CrossRefGoogle Scholar
  43. González-Miranda JM, 2007. Complex bifurcation structures in the Hindmarsh–Rose neuron model. International Journal of Bifurcation and Chaos, 17(9):3071–3083. MathSciNetzbMATHCrossRefGoogle Scholar
  44. Gu HG, Chen SG, 2014. Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker. Science China Technological Sciences, 57(5):864–871. CrossRefGoogle Scholar
  45. Gu HG, Pan BB, 2015. A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model. Nonlinear Dynamics, 81(4):2107–2126. MathSciNetCrossRefGoogle Scholar
  46. Gu HG, Pan BB, 2015. Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors. Frontiers in Computational Neuroscience, 9:108. CrossRefGoogle Scholar
  47. Gu HG, Pan BB, Chen GR, et al., 2014. Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dynamics, 78(1):391–407. MathSciNetCrossRefGoogle Scholar
  48. Gu HG, Pan BB, Xu J, 2014. Experimental observation of spike, burst and chaos synchronization of calcium concentration oscillations. EPL (Europhysics Letters), 106(5): 50003. CrossRefGoogle Scholar
  49. Gu HG, Pan BB, Li YY, 2015. The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain. Nonlinear Dynamics, 82(3):1191–1210. MathSciNetCrossRefGoogle Scholar
  50. Guo SL, Tang J, Ma J, et al., 2017. Autaptic modulation of electrical activity in a network of neuron-coupled astrocyte. Complexity, 2017:4631602. MathSciNetGoogle Scholar
  51. Hadfield J, Plank MJ, David T, 2013. Modeling secondary messenger pathways in neurovascular coupling. Bulletin of Mathematical Biology, 75(3):428–443. MathSciNetzbMATHCrossRefGoogle Scholar
  52. Halassa MM, Haydon PG, 2010. Integrated brain circuits: astrocytic networks modulate neuronal activity and behavior. Annual Review of Physiology, 72:335–355. CrossRefGoogle Scholar
  53. Hassard B, 1978. Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon. Journal of Theoretical Biology, 71(3):401–420. MathSciNetCrossRefGoogle Scholar
  54. Hayer A, Bhalla US, 2005. Molecular switches at the synapse emerge from receptor and kinase traffic. PLoS Computational Biology, 1(2):e20. CrossRefGoogle Scholar
  55. Henneberger C, Papouin T, Oliet SHR, et al., 2010. Long-term potentiation depends on release of D-serine from astrocytes. Nature, 463(7278):232–236. CrossRefGoogle Scholar
  56. Hodgkin AL, Huxley AF, 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4): 500–544.
  57. Höfer T, Venance L, Giaume C, 2002. Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach. Journal of Neuroscience, 22(12):4850–4859. CrossRefGoogle Scholar
  58. Holmes RM, Loew LM, 2008. Geometry shapes cell signaling network output. Chemistry & Biology, 15(6):523–524. CrossRefGoogle Scholar
  59. Holmes WR, Levy WB, 1990. Insights into associative long-term potentiation from computational models of NMDA receptor-mediated calcium influx and intracellular calcium concentration changes. Journal of Neurophysiology, 63(5):1148–1168.>CrossRefGoogle Scholar
  60. Hu XY, Liu CX, Liu L, et al., 2016. An electronic implementation for Morris–Lecar neuron model. Nonlinear Dynamics, 84(4):2317–2332. MathSciNetCrossRefGoogle Scholar
  61. Irvine JM, Blackwell KT, Alkon DL, et al., 1994. Angular separation in neural networks. Journal of Artificial Neural Networks, 1(1):169–182.Google Scholar
  62. Ito M, 1989. Long-term depression. Annual Review of Neuroscience, 12:85–102. CrossRefGoogle Scholar
  63. Jin WY, Wang A, Ma J, et al., 2019. Effects of electromagnetic induction and noise on the regulation of sleep wake cycle. Science China Technological Sciences, in press. Google Scholar
  64. Junge HJ, Rhee JS, Jahn O, et al., 2004. Calmodulin and Munc13 form a Ca2+ sensor/effector complex that controls short-term synaptic plasticity. Cell, 118(3):389–401. CrossRefGoogle Scholar
  65. Kawato M, Hamaguchi T, Murakami F, et al., 1984. Quantitative analysis of electrical properties of dendritic spines. Biological Cybernetics, 50(6):447–454. CrossRefGoogle Scholar
  66. Kenny A, Plank MJ, David T, 2018. The role of astrocytic calcium and TRPV4 channels in neurovascular coupling. Journal of Computational Neuroscience, 44(1):97–114. MathSciNetzbMATHCrossRefGoogle Scholar
  67. Khakh BS, Sofroniew MV, 2015. Diversity of astrocyte functions and phenotypes in neural circuits. Nature Neuroscience, 18(7):942–952. CrossRefGoogle Scholar
  68. Kim SY, Lim W, 2018. Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scalefree neuronal network. Cognitive Neurodynamics, 12(3): 315–342. CrossRefGoogle Scholar
  69. Kobe DH, 1986. Helmholtz’s theorem revisited. American Journal of Physics, 54(6):552–554. CrossRefGoogle Scholar
  70. Kotaleski JH, Blackwell KT, 2010. Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches. Nature Reviews Neuroscience, 11(4):239–251. CrossRefGoogle Scholar
  71. Lavrentovich M, Hemkin S, 2008. A mathematical model of spontaneous calcium(II) oscillations in astrocytes. Journal of Theoretical Biology, 251(4):553–560. MathSciNetzbMATHCrossRefGoogle Scholar
  72. Li XM, 2014. Signal integration on the dendrites of a pyramidal neuron model. Cognitive Neurodynamics, 8(1):81–85. CrossRefGoogle Scholar
  73. Li YX, Rinzel J, 1994. Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. Journal of Theoretical Biology, 166(4):461–473. CrossRefGoogle Scholar
  74. Lisman J, Goldring M, 1988. Evaluation of a model of long-term memory based on the properties of the Ca2+/ calmodulin-dependent protein kinase. Journal de Physiologie, 83(3):187–197.Google Scholar
  75. Lisman J, Goldring M, 1988. Feasibility of long-term storage of graded information by the Ca2+/calmodulin-dependent protein kinase molecules of the postsynaptic density. Proceedings of the National Academy of Sciences of the United States of America, 85(14):5320–5324. CrossRefGoogle Scholar
  76. Liu Y, Li CG, 2013. Stochastic resonance in feedforward-loop neuronal network motifs in astrocyte field. Journal of Theoretical Biology, 335:265–275. MathSciNetzbMATHCrossRefGoogle Scholar
  77. Liu Y, Ren GD, Zhou P, et al., 2019. Synchronization in networks of initially independent dynamical systems. Physica A: Statistical Mechanics and Its Applications, 520: 370–380. MathSciNetCrossRefGoogle Scholar
  78. Liu ZL, Ma J, Zhang G, et al., 2019. Synchronization control between two Chua’s circuits via capacitive coupling. Applied Mathematics and Computation, 360:94–106. MathSciNetCrossRefGoogle Scholar
  79. Liu ZL, Wang CN, Zhang G, et al., 2019. Synchronization between neural circuits connected by hybrid synapse. International Journal of Modern Physics B, 33(16): 1950170. MathSciNetCrossRefGoogle Scholar
  80. Lu LL, Jia Y, Liu WH, et al., 2017. Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. Complexity, 2017:7628537. MathSciNetzbMATHGoogle Scholar
  81. Lu LL, Jia Y, Kirunda JB, et al., 2019. Effects of noise and synaptic weight on propagation of subthreshold excitatory postsynaptic current signal in a feed-forward neural network. Nonlinear Dynamics, 95(2):1673–1686. CrossRefGoogle Scholar
  82. Lv M, Ma J, Yao YG, et al., 2019. Synchronization and wave propagation in neuronal network under field coupling. Science China Technological Sciences, 62(3):448–457. CrossRefGoogle Scholar
  83. Ma J, Tang J, 2015. A review for dynamics of collective behaviors of network of neurons. Science China Technological Sciences, 58(12):2038–2045. CrossRefGoogle Scholar
  84. Ma J, Qin HX, Song XL, et al., 2015. Pattern selection in neuronal network driven by electric autapses with diversity in time delays. International Journal of Modern Physics B, 29(1):1450239. CrossRefGoogle Scholar
  85. Ma J, Song XL, Tang J, et al., 2015. Wave emitting and propagation induced by autapse in a forward feedback neuronal network. Neurocomputing, 167:378–389. CrossRefGoogle Scholar
  86. Ma J, Xu Y, Wang CN, et al., 2016. Pattern selection and self-organization induced by random boundary initial values in a neuronal network. Physica A: Statistical Mechanics and Its Applications, 461:586–594. MathSciNetzbMATHCrossRefGoogle Scholar
  87. Ma J, Xu Y, Ren GD, et al., 2016. Prediction for breakup of spiral wave in a regular neuronal network. Nonlinear Dynamics, 84(2):497–509. MathSciNetCrossRefGoogle Scholar
  88. Ma J, Wu FQ, Hayat T, et al., 2017. Electromagnetic induction and radiation-induced abnormality of wave propagation in excitable media. Physica A: Statistical Mechanics and Its Applications, 486:508–516. MathSciNetCrossRefGoogle Scholar
  89. Ma J, Zhang G, Hayat T, et al., 2019. Model electrical activity of neuron under electric field. Nonlinear Dynamics, 95: 1585–1598.
  90. Ma SY, Yao Z, Zhang Y, et al., 2019. Phase synchronization and lock between memristive circuits under field coupling. AEU-International Journal of Electronics and Communications, 105:177–185. CrossRefGoogle Scholar
  91. Malenka RC, Bear MF, 2004. LTP and LTD: an embarrassment of riches. Neuron, 44(1):5–21. CrossRefGoogle Scholar
  92. Manninen T, Hituri K, Kotaleski JH, et al., 2010. Postsynaptic signal transduction models for long-term potentiation and depression. Frontiers in Computational Neuroscience, 4:152. CrossRefGoogle Scholar
  93. Manninen T, Havela R, Linne ML, 2018. Computational models for calcium-mediated astrocyte functions. Frontiers in Computational Neuroscience, 12:14. CrossRefGoogle Scholar
  94. Mao XC, 2017. Complicated dynamics of a ring of nonidentical FitzHugh–Nagumo neurons with delayed couplings. Nonlinear Dynamics, 87(4):2395–2406. MathSciNetzbMATHCrossRefGoogle Scholar
  95. McCormick DA, Shu YS, Yu YG, 2007. Neurophysiology: Hodgkin and Huxley model—still standing? Nature, 445(7123):E1-E2. Google Scholar
  96. Mei GF, Wu XQ, Ning D, et al., 2016. Finite-time stabilization of complex dynamical networks via optimal control. Complexity, 21(S1):417–425. Google Scholar
  97. Mei GF, Wu XQ, Wang YF, et al., 2018. Compressivesensing-based structure identification for multilayer networks. IEEE Transactions on Cybernetics, 48(2):754–764. CrossRefGoogle Scholar
  98. Mesiti F, Floor PA, Balasingham I, 2015. Astrocyte to neuron communication channels with applications. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 1(2):164–175. CrossRefGoogle Scholar
  99. Morris C, Lecar H, 1981. Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35(1):193–213. CrossRefGoogle Scholar
  100. Mostaghimi S, Nazarimehr F, Jafari S, et al., 2019. Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow. Applied Mathematics and Computation, 348:42–56. MathSciNetCrossRefGoogle Scholar
  101. Mvogo A, Takembo CN, Ekobena Fouda HP, et al., 2017. Pattern formation in diffusive excitable systems under magnetic flow effects. Physics Letters A, 381(28):2264–2271. MathSciNetCrossRefGoogle Scholar
  102. Nadkarni S, Jung P, 2003. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? Physical Review Letters, 91(26):268101. CrossRefGoogle Scholar
  103. Nadkarni S, Jung P, 2007. Modeling synaptic transmission of the tripartite synapse. Physical Biology, 4(1):1–9. CrossRefGoogle Scholar
  104. Navarrete M, Díez A, Araque A, 2014. Astrocytes in endocannabinoid signalling. Philosophical Transactions of the Royal Society B: Biological Sciences, 369(1654): 20130599. CrossRefGoogle Scholar
  105. Nazari S, Faez K, Amiri M, 2017. A multiplier-less digital design of a bio-inspired stimulator to suppress synchronized regime in a large-scale, sparsely connected neural network. Neural Computing and Applications, 28(2):375–390. CrossRefGoogle Scholar
  106. Nestler EJ, 2001. Molecular basis of long-term plasticity underlying addiction. Nature Reviews Neuroscience, 2(2): 119–128. CrossRefGoogle Scholar
  107. Neves SR, Tsokas P, Sarkar A, et al., 2008. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell, 133(4):666–680. CrossRefGoogle Scholar
  108. Newman EA, Zahs KR, 1997. Calcium waves in retinal glial cells. Science, 275(5301):844–847. CrossRefGoogle Scholar
  109. Pan B, Zucker RS, 2009. A general model of synaptic transmission and short-term plasticity. Neuron, 62(4):539–554. CrossRefGoogle Scholar
  110. Park S, Chu M, Kim J, et al., 2015. Electronic system with memristive synapses for pattern recognition. Scientific Reports, 5:10123. CrossRefGoogle Scholar
  111. Parpura V, Basarsky TA, Liu F, et al., 1994. Glutamatemediated astrocyte–neuron signalling. Nature, 369(6483): 744–747. CrossRefGoogle Scholar
  112. Patel GN, DeWeerth SP, 1997. Analogue VLSI morris-lecar neuron. Electronics Letters, 33(12):997–998. CrossRefGoogle Scholar
  113. Pellionisz AJ, 1989. Neural geometry: towards a fractal model of neurons. In: Cotterill RMJ (Ed.), Models of Brain Function. Cambridge University Press, Cambridge, UK, p.453–464.Google Scholar
  114. Perea G, Navarrete M, Araque A, 2009. Tripartite synapses: astrocytes process and control synaptic information. Trends in Neurosciences, 32(8):421–431. CrossRefGoogle Scholar
  115. Poskanzer KE, Yuste R, 2016. Astrocytes regulate cortical state switching in vivo. Proceedings of the National Academy of Sciences of the United States of America, 113(19):E2675–E2684. CrossRefGoogle Scholar
  116. Pospischil M, Toledo-Rodriguez M, Monier C, et al., 2008. Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons. Biological Cybernetics, 99(4–5):427–441. MathSciNetzbMATHCrossRefGoogle Scholar
  117. Postnov DE, Ryazanova LS, Sosnovtseva OV, 2007. Functional modeling of neural-glial interaction. Biosystems, 89(1–3):84–91. CrossRefGoogle Scholar
  118. Qin HX, Ma J, Jin WY, et al., 2014. Dynamics of electric activities in neuron and neurons of network induced by autapses. Science China Technological Sciences, 57(5): 936–946. CrossRefGoogle Scholar
  119. Qu ZL, Hu G, Garfinkel A, et al., 2014. Nonlinear and stochastic dynamics in the heart. Physics Reports, 543(2): 61–162.
  120. Ren GD, Zhou P, Ma J, et al., 2017. Dynamical response of electrical activities in digital neuron circuit driven by autapse. International Journal of Bifurcation and Chaos, 27(12):1750187. MathSciNetCrossRefGoogle Scholar
  121. Rostami Z, Pham VT, Jafari S, et al., 2018. Taking control of initiated propagating wave in a neuronal network using magnetic radiation. Applied Mathematics and Computation, 338:141–151. MathSciNetCrossRefGoogle Scholar
  122. Salin PA, Scanziani M, Malenka RC, et al., 1996. Distinct short-term plasticity at two excitatory synapses in the hippocampus. Proceedings of the National Academy of Sciences of the United States of America, 93(23):13304–13309. CrossRefGoogle Scholar
  123. Schiegg A, Gerstner W, Ritz R, et al., 1985. Intracellular Ca2+ stores can account for the time course of LTP induction: a model of Ca2+ dynamics in dendritic spines. American Physiological Society, 74(3):1046–1055. Google Scholar
  124. Seung HS, Lee DD, Reis BY, et al., 2000. The autapse: a simple illustration of short-term analog memory storage by tuned synaptic feedback. Journal of Computational Neuroscience, 9(2):171–185. zbMATHCrossRefGoogle Scholar
  125. Sharma SK, Haobijam D, Singh SS, et al., 2019. Neuronal communication: stochastic neuron dynamics and multisynchrony states. AEU-International Journal of Electronics and Communications, 100:75–85. CrossRefGoogle Scholar
  126. Sloan SA, Barres BA, 2014. Looks can be deceiving: reconsidering the evidence for gliotransmission. Neuron, 84(6): 1112–1115.
  127. Song XL, Wang CN, Ma J, et al., 2015. Transition of electric activity of neurons induced by chemical and electric autapses. Science China Technological Sciences, 58(6): 1007–1014. CrossRefGoogle Scholar
  128. Song XL, Wang HT, Chen Y, 2018. Coherence resonance in an autaptic Hodgkin–Huxley neuron with time delay. Nonlinear Dynamics, 94(1):141–150. CrossRefGoogle Scholar
  129. Stent GS, 1984. Semantics and neural development. In: Sharma CS (Ed.), Organizing Principles of Neural Development. Springer, Boston, USA, p.145–160. CrossRefGoogle Scholar
  130. Storace M, Linaro D, de Lange E, 2008. The Hindmarsh–Rose neuron model: bifurcation analysis and piecewise-linear approximations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 18(3):033128. MathSciNetCrossRefGoogle Scholar
  131. Sun XJ, Liu ZF, Perc M, 2019. Effects of coupling strength and network topology on signal detection in small-world neuronal networks. Nonlinear Dynamics, 96(3):2145–2155. CrossRefGoogle Scholar
  132. Takembo CN, Mvogo A, Ekobena Fouda HP, et al., 2018. Modulated wave formation in myocardial cells under electromagnetic radiation. International Journal of Modern Physics B, 32(14):1850165. MathSciNetCrossRefGoogle Scholar
  133. Tamaševičius A, Mykolaitis G, Tamaševičiūtė E, et al., 2015. Two-terminal feedback circuit for suppressing synchrony of the FitzHugh-Nagumo oscillators. Nonlinear Dynamics, 81(1–2):783–788. CrossRefGoogle Scholar
  134. Tang J, Luo JM, Ma J, 2013. Information transmission in a neuron-astrocyte coupled model. PLoS One, 8(11): e80324. CrossRefGoogle Scholar
  135. Tang J, Liu TB, Ma J, et al., 2016. Effect of calcium channel noise in astrocytes on neuronal transmission. Communications in Nonlinear Science and Numerical Simulation, 32:262–272. MathSciNetCrossRefGoogle Scholar
  136. Tang J, Zhang J, Ma J, et al., 2017. Astrocyte calcium wave induces seizure-like behavior in neuron network. Science China Technological Sciences, 60(7):1011–1018. CrossRefGoogle Scholar
  137. Tarai S, Mukherjee R, Gupta S, et al., 2019. Influence of pharmacological and epigenetic factors to suppress neurotrophic factors and enhance neural plasticity in stress and mood disorders. Cognitive Neurodynamics, 13(3): 219–237. CrossRefGoogle Scholar
  138. Toivari E, Manninen T, Nahata AK, et al., 2011. Effects of transmitters and amyloid-beta peptide on calcium signals in rat cortical astrocytes: Fura-2AM measurements and stochastic model simulations. PLoS One, 6(3):e17914. CrossRefGoogle Scholar
  139. Tomba C, Braïni C, Wu BL, et al., 2014. Tuning the adhesive geometry of neurons: length and polarity control. Soft Matter, 10(14):2381–2387. CrossRefGoogle Scholar
  140. Trachtenberg JT, Chen BE, Knott GW, et al., 2002. Long-term in vivo imaging of experience-dependent synaptic plasticity in adult cortex. Nature, 420(6917):788–794. CrossRefGoogle Scholar
  141. Tsumoto K, Kitajima H, Yoshinaga T, et al., 2006. Bifurcations in Morris–Lecar neuron model. Neurocomputing, 69(4–6):293–316. CrossRefGoogle Scholar
  142. Tutkun E, Ayyildiz M, Agar E, 2010. Short-duration swimming exercise decreases penicillin-induced epileptiform ECoG activity in rats. Acta Neurobiologiae Experimentalis, 70(4):382–389.Google Scholar
  143. Ursino M, Cuppini C, Cappa SF, et al., 2018. A feature-based neurocomputational model of semantic memory. Cognitive Neurodynamics, 12(6):525–547. CrossRefGoogle Scholar
  144. Uzun R, 2017. Influences of autapse and channel blockage on multiple coherence resonance in a single neuron. Applied Mathematics and Computation, 315:203–210. MathSciNetzbMATHCrossRefGoogle Scholar
  145. Uzun R, Yilmaz E, Ozer M, 2017. Effects of autapse and ion channel block on the collective firing activity of Newman–Watts small-world neuronal networks. Physica A: Statistical Mechanics and Its Applications, 486:386–396. MathSciNetCrossRefGoogle Scholar
  146. Valverde F, 1976. Aspects of cortical organization related to the geometry of neurons with intra-cortical axons. Journal of Neurocytology, 5(5):509–529. CrossRefGoogle Scholar
  147. van der Loos H, Glaser EM, 1972. Autapses in neocortex cerebri: synapses between a pyramidal cell’s axon and its own dendrites. Brain Research, 48:355–360. CrossRefGoogle Scholar
  148. Volterra A, Meldolesi J, 2005. Astrocytes, from brain glue to communication elements: the revolution continues. Nature Reviews Neuroscience, 6(8):626–640. CrossRefGoogle Scholar
  149. Wade J, McDaid L, Harkin J, et al., 2012. Self-repair in a bidirectionally coupled astrocyte-neuron (AN) system based on retrograde signaling. Frontiers in Computational Neuroscience, 6:76. CrossRefGoogle Scholar
  150. Wang CN, Ma J, 2018. A review and guidance for pattern selection in spatiotemporal system. International Journal of Modern Physics B, 32(6):1830003. MathSciNetCrossRefGoogle Scholar
  151. Wang CN, Guo SL, Xu Y, et al., 2017. Formation of autapse connected to neuron and its biological function. Complexity, 2017:5436737. MathSciNetzbMATHGoogle Scholar
  152. Wang JY, Yang XL, Sun ZK, 2018. Suppressing bursting synchronization in a modular neuronal network with synaptic plasticity. Cognitive Neurodynamics, 12(6):625–636. CrossRefGoogle Scholar
  153. Wang RB, Wang ZY, Zhu ZY, 2018. The essence of neuronal activity from the consistency of two different neuron models. Nonlinear Dynamics, 92(3):973–982. MathSciNetCrossRefGoogle Scholar
  154. Wang XH, Takano T, Nedergaard M, 2009. Astrocytic calcium signaling: mechanism and implications for functional brain imaging. In: Hyder F (Ed.), Dynamic Brain Imaging: Multi-modal Methods and in vivo Applications. Humana Press, New York, USA, p.93–109.
  155. Wang Y, Wang CN, Ren GD, et al., 2017. Energy dependence on modes of electric activities of neuron driven by multichannel signals. Nonlinear Dynamics, 89(3):1967–1987. CrossRefGoogle Scholar
  156. Wang YH, Wang RB, Xu XY, 2017. Neural energy supplyconsumption properties based on Hodgkin-Huxley model. Neural Plasticity, 2017:6207141. Google Scholar
  157. Wang YY, Wang RB, 2018. An improved neuronal energy model that better captures of dynamic property of neuronal activity. Nonlinear Dynamics, 91(1):319–327. CrossRefGoogle Scholar
  158. Wang ZY, Wang RB, Fang RY, 2015. Energy coding in neural network with inhibitory neurons. Cognitive Neurodynamics, 9(2):129–144. MathSciNetCrossRefGoogle Scholar
  159. Wei H, Bu YJ, Dai DW, 2017. A decision-making model based on a spiking neural circuit and synaptic plasticity. Cognitive Neurodynamics, 11(5):415–431. CrossRefGoogle Scholar
  160. Wei X, Wu XQ, Chen SH, et al., 2018. Cooperative epidemic spreading on a two-layered interconnected network. SIAM Journal on Applied Dynamical Systems, 17(2): 1503–1520. MathSciNetzbMATHCrossRefGoogle Scholar
  161. Witthoft A, Karniadakis GE, 2012. A bidirectional model for communication in the neurovascular unit. Journal of Theoretical Biology, 311:80–93. MathSciNetzbMATHCrossRefGoogle Scholar
  162. Witthoft A, Filosa JA, Karniadakis GE, 2013. Potassium buffering in the neurovascular unit: models and sensitivity analysis. Biophysical Journal, 105(9):2046–2054. CrossRefGoogle Scholar
  163. Wu FQ, Wang CN, Xu Y, et al., 2016. Model of electrical activity in cardiac tissue under electromagnetic induction. Scientific Reports, 6:28. CrossRefGoogle Scholar
  164. Wu FQ, Wang CN, Jin WY, et al., 2017. Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Physica A: Statistical Mechanics and Its Applications, 469:81–88. MathSciNetzbMATHCrossRefGoogle Scholar
  165. Wu FQ, Hayat T, An XL, et al., 2018. Can Hamilton energy feedback suppress the chameleon chaotic flow? Nonlinear Dynamics, 94(1):669–677. CrossRefGoogle Scholar
  166. Wu FQ, Zhou P, Alsaedi A, et al., 2018. Synchronization dependence on initial setting of chaotic systems without equilibria. Chaos, Solitons & Fractals, 110:124–132. MathSciNetCrossRefGoogle Scholar
  167. Wu FQ, Ma J, Ren GD, 2018. Synchronization stability between initial-dependent oscillators with periodical and chaotic oscillation. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 19(12): 889–903. CrossRefGoogle Scholar
  168. Wu FQ, Ma J, Zhang G, 2019. A new neuron model under electromagnetic field. Applied Mathematics and Computation, 347:590–599. MathSciNetCrossRefGoogle Scholar
  169. Xiao WW, Gu HG, Liu MR, 2016. Spatiotemporal dynamics in a network composed of neurons with different excitabilities and excitatory coupling. Science China Technological Sciences, 59(12):1943–1952. CrossRefGoogle Scholar
  170. Xu F, Zhang JQ, Fang TT, et al., 2018. Synchronous dynamics in neural system coupled with memristive synapse. Nonlinear Dynamics, 92(3):1395–1402. CrossRefGoogle Scholar
  171. Xu Q, Song Z, Bao H, et al., 2018. Two-neuron-based non-autonomous memristive Hopfield neural network: numerical analyses and hardware experiments. AEUInternational Journal of Electronics and Communications, 96:66–74. CrossRefGoogle Scholar
  172. Xu Y, Wang CN, Lv M, et al., 2016. Local pacing, noise induced ordered wave in a 2D lattice of neurons. Neurocomputing, 207:398–407. CrossRefGoogle Scholar
  173. Xu Y, Jia Y, Kirunda JB, et al., 2018. Dynamic behaviors in coupled neuron system with the excitatory and inhibitory autapse under electromagnetic induction. Complexity, 2018:3012743. Google Scholar
  174. Xu Y, Jia Y, Ge MY, et al., 2018. Effects of ion channel blocks on electrical activity of stochastic Hodgkin–Huxley neural network under electromagnetic induction. Neurocomputing, 283:196–204. CrossRefGoogle Scholar
  175. Xu YM, Yao Z, Hobiny A, et al., 2019. Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits. Frontiers of Information Technology & Electronic Engineering, 20(4):571–583. CrossRefGoogle Scholar
  176. Yang XL, Yu YH, Sun ZK, 2017. Autapse-induced multiple stochastic resonances in a modular neuronal network. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(8):083117. MathSciNetCrossRefGoogle Scholar
  177. Yang YQ, Yeo CK, 2015. Conceptual network model from sensory neurons to astrocytes of the human nervous system. IEEE Transactions on Biomedical Engineering, 62(7):1843–1852. CrossRefGoogle Scholar
  178. Yao Z, Ma J, Yao YG, et al., 2019. Synchronization realization between two nonlinear circuits via an induction coil coupling. Nonlinear Dynamics, 96(1):205–217. CrossRefGoogle Scholar
  179. Yue Y, Liu LW, Liu YJ, et al., 2017. Dynamical response, information transition and energy dependence in a neuron model driven by autapse. Nonlinear Dynamics, 90(4): 2893–2902. CrossRefGoogle Scholar
  180. Yuste R, Bonhoeffer T, 2001. Morphological changes in dendritic spines associated with long-term synaptic plasticity. Annual Review of Neuroscience, 24:1071–1089. CrossRefGoogle Scholar
  181. Zayer F, Dghais W, Benabdeladhim M, et al., 2019. Low power, ultrafast synaptic plasticity in 1R-ferroelectric tunnel memristive structure for spiking neural networks. AEU-International Journal of Electronics and Communications, 100:56–65. CrossRefGoogle Scholar
  182. Zeng S, Li B, Chen SQ, 2009. Simulation of spontaneous Ca2+ oscillations in astrocytes mediated by voltage-gated calcium channels. Biophysical Journal, 97(9):2429–2437. CrossRefGoogle Scholar
  183. Zhan FB, Liu SQ, 2017. Response of electrical activity in an improved neuron model under electromagnetic radiation and noise. Frontiers in Computational Neuroscience, 11:107. CrossRefGoogle Scholar
  184. Zhang G, Wang CN, Alsaedi A, et al., 2018. Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system. Kybernetika, 54(4):648–663. MathSciNetzbMATHGoogle Scholar
  185. Zhang JH, Liao XF, 2017. Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse. AEU-International Journal of Electronics and Communications, 75:82–90. CrossRefGoogle Scholar
  186. Zhao ZG, Gu HG, 2015. The influence of single neuron dynamics and network topology on time delay-induced multiple synchronous behaviors in inhibitory coupled network. Chaos, Solitons & Fractals, 80:96–108. MathSciNetzbMATHCrossRefGoogle Scholar
  187. Zhao ZG, Gu HG, 2017. Transitions between classes of neuronal excitability and bifurcations induced by autapse. Scientific Reports, 7(1):6760. CrossRefGoogle Scholar
  188. Zheng HW, Wang RB, Qu JY, 2016. Effect of different glucose supply conditions on neuronal energy metabolism. Cognitive Neurodynamics, 10(6):563–571. CrossRefGoogle Scholar
  189. Zonta M, Angulo MC, Gobbo S, et al., 2003. Neuron-toastrocyte signaling is central to the dynamic control of brain microcirculation. Nature Neuroscience, 6(1):43–50. CrossRefGoogle Scholar
  190. Zucker RS, 1989. Short-term synaptic plasticity. Annual Review of Neuroscience, 12:13–31. CrossRefGoogle Scholar
  191. Zucker RS, Regehr WG, 2002. Short-term synaptic plasticity. Annual Review of Physiology, 64:355–405. CrossRefGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  2. 2.School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  3. 3.Department of PhysicsCentral China Normal UniversityWuhanChina
  4. 4.School of PhysicsChina University of Mining and TechnologyXuzhouChina

Personalised recommendations