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Abstract: 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.

Authors have presented a detail review of neuron model, astrocyte, synaptic plasticity, collective behaviors in neural networks from a physical view point. Different examples have been proposed to illustrate authors' aim. The manuscript is attractive.

从物理学角度认知计算神经动力学

[1]Abbott LF, Nelson SB, 2000. Synaptic plasticity: taming the beast. Nature Neuroscience, 3(11):1178-1183.

[2]Abraham WC, Bear MF, 1996. Metaplasticity: the plasticity of synaptic plasticity. Trends in Neurosciences, 19(4):126-130.

[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.

[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.

[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.

[6]Amiri M, Bahrami F, Janahmadi M, 2012a. Functional contributions of astrocytes in synchronization of a neuronal network model. Journal of Theoretical Biology, 292:60-70.

[7]Amiri M, Bahrami F, Janahmadi M, 2012b. Modified thalamocortical model: a step towards more understanding of the functional contribution of astrocytes to epilepsy. Journal of Computational Neuroscience, 33(2):285-299.

[8]Amiri M, Bahrami F, Janahmadi M, 2012c. On the role of astrocytes in epilepsy: a functional modeling approach. Neuroscience Research, 72(2):172-180.

[9]Amiri M, Hosseinmardi N, Bahrami F, et al., 2013. Astrocyte-neuron 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.

[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.

[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.

[13]Bear MF, Malenka RC, 1994. Synaptic plasticity: LTP and LTD. Current Opinion in Neurobiology, 4(3):389-399.

[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.

[15]Bezprozvanny I, Watras J, Ehrlich BE, 1991. Bell-shaped calcium-response curves of Ins(1,4,5)P₃- and calcium-gated channels from endoplasmic reticulum of cerebellum. Nature, 351(6329):751-754.

[16]Bhalla US, 2002. Mechanisms for temporal tuning and filtering by postsynaptic signaling pathways. Biophysical Journal, 83(2):740-752.

[17]Bhalla US, 2004. Signaling in small subcellular volumes. II. Stochastic and diffusion effects on synaptic network properties. Biophysical Journal, 87(2):745-753.

[18]Bhalla US, Iyengar R, 1999. Emergent properties of networks of biological signaling pathways. Science, 283(5400):381-387.

[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.

[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.

[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.

[22]Bliss TVP, Collingridge GL, 1993. A synaptic model of memory: long-term potentiation in the hippocampus. Nature, 361(6407):31-39.

[23]Bui L, Glavinović MI, 2013. Synaptic activity slows vesicular replenishment at excitatory synapses of rat hippocampus. Cognitive Neurodynamics, 7(2):105-120.

[24]Buonomano DV, 2000. Decoding temporal information: a model based on short-term synaptic plasticity. Journal of Neuroscience, 20(3):1129-1141.

[25]Busciglio J, Lorenzo A, Yankner BA, 1992. Methodological variables in the assessment of beta amyloid neurotoxicity. Neurobiology of Aging, 13(5):609-612.

[26]Carro-Pérez I, Sánchez-López C, González-Hernández HG, 2018. Experimental verification of a memristive neural network. Nonlinear Dynamics, 93(4):1823-1840.

[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.

[28]Chander BS, Chakravarthy VS, 2012. A computational model of neuro-glio-vascular loop interactions. PLoS One, 7(11):e48802.

[29]Coba MP, Pocklington AJ, Collins MO, et al., 2009. Neurotransmitters drive combinatorial multistate postsynaptic density networks. Science Signaling, 2(68):ra19.

[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.

[31]Covi E, Brivio S, Serb A, et al., 2016. Analog memristive synapse in spiking networks implementing unsupervised learning. Frontiers in Neuroscience, 10:482.

[32]Dani JW, Chernjavsky A, Smith SJ, 1992. Neuronal activity triggers calcium waves in hippocampal astrocyte networks. Neuron, 8(3):429-440.

[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.

[34]de Young GW, Keizer J, 1992. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca²⁺ concentration. Proceedings of the National Academy of Sciences of the United States of America, 89(20):9895-9899.

[35]Engert F, Bonhoeffer T, 1999. Dendritic spine changes associated with hippocampal long-term synaptic plasticity. Nature, 399(6731):66-70.

[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.

[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.

[38]Ge MY, Xu Y, Zhang ZK, et al., 2018a. Autaptic modulation-induced neuronal electrical activities and wave propagation on network under electromagnetic induction. The European Physical Journal Special Topics, 227(7-9):799-809.

[39]Ge MY, Jia Y, Xu Y, et al., 2018b. 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.

[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.

[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.

[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.

[43]González-Miranda JM, 2007. Complex bifurcation structures in the Hindmarsh–Rose neuron model. International Journal of Bifurcation and Chaos, 17(9):3071-3083.

[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.

[45]Gu HG, Pan BB, 2015a. 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.

[46]Gu HG, Pan BB, 2015b. Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors. Frontiers in Computational Neuroscience, 9:108.

[47]Gu HG, Pan BB, Chen GR, et al., 2014a. Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dynamics, 78(1):391-407.

[48]Gu HG, Pan BB, Xu J, 2014b. Experimental observation of spike, burst and chaos synchronization of calcium concentration oscillations. EPL (Europhysics Letters), 106(5):50003.

[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.

[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.

[51]Hadfield J, Plank MJ, David T, 2013. Modeling secondary messenger pathways in neurovascular coupling. Bulletin of Mathematical Biology, 75(3):428-443.

[52]Halassa MM, Haydon PG, 2010. Integrated brain circuits: astrocytic networks modulate neuronal activity and behavior. Annual Review of Physiology, 72:335-355.

[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.

[54]Hayer A, Bhalla US, 2005. Molecular switches at the synapse emerge from receptor and kinase traffic. PLoS Computational Biology, 1(2):e20.

[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.

[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.

[58]Holmes RM, Loew LM, 2008. Geometry shapes cell signaling network output. Chemistry & Biology, 15(6):523-524.

[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.

[60]Hu XY, Liu CX, Liu L, et al., 2016. An electronic implementation for Morris–Lecar neuron model. Nonlinear Dynamics, 84(4):2317-2332.

[61]Irvine JM, Blackwell KT, Alkon DL, et al., 1994. Angular separation in neural networks. Journal of Artificial Neural Networks, 1(1):169-182.

[62]Ito M, 1989. Long-term depression. Annual Review of Neuroscience, 12:85-102.

[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.

[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.

[65]Kawato M, Hamaguchi T, Murakami F, et al., 1984. Quantitative analysis of electrical properties of dendritic spines. Biological Cybernetics, 50(6):447-454.

[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.

[67]Khakh BS, Sofroniew MV, 2015. Diversity of astrocyte functions and phenotypes in neural circuits. Nature Neuroscience, 18(7):942-952.

[68]Kim SY, Lim W, 2018. Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cognitive Neurodynamics, 12(3):315-342.

[69]Kobe DH, 1986. Helmholtz’s theorem revisited. American Journal of Physics, 54(6):552-554.

[70]Kotaleski JH, Blackwell KT, 2010. Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches. Nature Reviews Neuroscience, 11(4):239-251.

[71]Lavrentovich M, Hemkin S, 2008. A mathematical model of spontaneous calcium(II) oscillations in astrocytes. Journal of Theoretical Biology, 251(4):553-560.

[72]Li XM, 2014. Signal integration on the dendrites of a pyramidal neuron model. Cognitive Neurodynamics, 8(1):81-85.

[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.

[74]Lisman J, Goldring M, 1988a. 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.

[75]Lisman J, Goldring M, 1988b. 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.

[76]Liu Y, Li CG, 2013. Stochastic resonance in feedforward-loop neuronal network motifs in astrocyte field. Journal of Theoretical Biology, 335:265-275.

[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.

[78]Liu ZL, Ma J, Zhang G, et al., 2019a. Synchronization control between two Chua’s circuits via capacitive coupling. Applied Mathematics and Computation, 360:94-106.

[79]Liu ZL, Wang CN, Zhang G, et al., 2019b. Synchronization between neural circuits connected by hybrid synapse. International Journal of Modern Physics B, 33(16):1950170.

[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.

[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.

[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.

[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.

[84]Ma J, Qin HX, Song XL, et al., 2015a. Pattern selection in neuronal network driven by electric autapses with diversity in time delays. International Journal of Modern Physics B, 29(1):1450239.

[85]Ma J, Song XL, Tang J, et al., 2015b. Wave emitting and propagation induced by autapse in a forward feedback neuronal network. Neurocomputing, 167:378-389.

[86]Ma J, Xu Y, Wang CN, et al., 2016a. 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.

[87]Ma J, Xu Y, Ren GD, et al., 2016b. Prediction for breakup of spiral wave in a regular neuronal network. Nonlinear Dynamics, 84(2):497-509.

[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.

[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.

[91]Malenka RC, Bear MF, 2004. LTP and LTD: an embarrassment of riches. Neuron, 44(1):5-21.

[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.

[93]Manninen T, Havela R, Linne ML, 2018. Computational models for calcium-mediated astrocyte functions. Frontiers in Computational Neuroscience, 12:14.

[94]Mao XC, 2017. Complicated dynamics of a ring of nonidentical FitzHugh–Nagumo neurons with delayed couplings. Nonlinear Dynamics, 87(4):2395-2406.

[95]McCormick DA, Shu YS, Yu YG, 2007. Neurophysiology: Hodgkin and Huxley model—still standing? Nature, 445(7123):E1-E2.

[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.

[97]Mei GF, Wu XQ, Wang YF, et al., 2018. Compressive-sensing-based structure identification for multilayer networks. IEEE Transactions on Cybernetics, 48(2):754-764.

[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.

[99]Morris C, Lecar H, 1981. Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35(1):193-213.

[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.

[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.

[102]Nadkarni S, Jung P, 2003. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? Physical Review Letters, 91(26):268101.

[103]Nadkarni S, Jung P, 2007. Modeling synaptic transmission of the tripartite synapse. Physical Biology, 4(1):1-9.

[104]Navarrete M, Díez A, Araque A, 2014. Astrocytes in endocannabinoid signalling. Philosophical Transactions of the Royal Society B: Biological Sciences, 369(1654):20130599.

[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.

[106]Nestler EJ, 2001. Molecular basis of long-term plasticity underlying addiction. Nature Reviews Neuroscience, 2(2):119-128.

[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.

[108]Newman EA, Zahs KR, 1997. Calcium waves in retinal glial cells. Science, 275(5301):844-847.

[109]Pan B, Zucker RS, 2009. A general model of synaptic transmission and short-term plasticity. Neuron, 62(4):539-554.

[110]Park S, Chu M, Kim J, et al., 2015. Electronic system with memristive synapses for pattern recognition. Scientific Reports, 5:10123.

[111]Parpura V, Basarsky TA, Liu F, et al., 1994. Glutamate-mediated astrocyte–neuron signalling. Nature, 369(6483):744-747.

[112]Patel GN, DeWeerth SP, 1997. Analogue VLSI morris-lecar neuron. Electronics Letters, 33(12):997-998.

[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.

[114]Perea G, Navarrete M, Araque A, 2009. Tripartite synapses: astrocytes process and control synaptic information. Trends in Neurosciences, 32(8):421-431.

[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.

[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.

[117]Postnov DE, Ryazanova LS, Sosnovtseva OV, 2007. Functional modeling of neural-glial interaction. Biosystems, 89(1-3):84-91.

[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.

[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.

[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.

[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.

[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.

[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.

[125]Sharma SK, Haobijam D, Singh SS, et al., 2019. Neuronal communication: stochastic neuron dynamics and multi-synchrony states. AEU-International Journal of Electronics and Communications, 100:75-85.

[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.

[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.

[129]Stent GS, 1984. Semantics and neural development. In: Sharma CS (Ed.), Organizing Principles of Neural Development. Springer, Boston, USA, p.145-160.

[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.

[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.

[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.

[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.

[134]Tang J, Luo JM, Ma J, 2013. Information transmission in a neuron-astrocyte coupled model. PLoS One, 8(11):e80324.

[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.

[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.

[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.

[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.

[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.

[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.

[141]Tsumoto K, Kitajima H, Yoshinaga T, et al., 2006. Bifurcations in Morris–Lecar neuron model. Neurocomputing, 69(4-6):293-316.

[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.

[143]Ursino M, Cuppini C, Cappa SF, et al., 2018. A feature-based neurocomputational model of semantic memory. Cognitive Neurodynamics, 12(6):525-547.

[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.

[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.

[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.

[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.

[148]Volterra A, Meldolesi J, 2005. Astrocytes, from brain glue to communication elements: the revolution continues. Nature Reviews Neuroscience, 6(8):626-640.

[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.

[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.

[151]Wang CN, Guo SL, Xu Y, et al., 2017. Formation of autapse connected to neuron and its biological function. Complexity, 2017:5436737.

[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.

[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.

[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 multi-channel signals. Nonlinear Dynamics, 89(3):1967-1987.

[156]Wang YH, Wang RB, Xu XY, 2017. Neural energy supply-consumption properties based on Hodgkin-Huxley model. Neural Plasticity, 2017:6207141.

[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.

[158]Wang ZY, Wang RB, Fang RY, 2015. Energy coding in neural network with inhibitory neurons. Cognitive Neurodynamics, 9(2):129-144.

[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.

[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.

[161]Witthoft A, Karniadakis GE, 2012. A bidirectional model for communication in the neurovascular unit. Journal of Theoretical Biology, 311:80-93.

[162]Witthoft A, Filosa JA, Karniadakis GE, 2013. Potassium buffering in the neurovascular unit: models and sensitivity analysis. Biophysical Journal, 105(9):2046-2054.

[163]Wu FQ, Wang CN, Xu Y, et al., 2016. Model of electrical activity in cardiac tissue under electromagnetic induction. Scientific Reports, 6:28.

[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.

[165]Wu FQ, Hayat T, An XL, et al., 2018a. Can Hamilton energy feedback suppress the chameleon chaotic flow? Nonlinear Dynamics, 94(1):669-677.

[166]Wu FQ, Zhou P, Alsaedi A, et al., 2018b. Synchronization dependence on initial setting of chaotic systems without equilibria. Chaos, Solitons & Fractals, 110:124-132.

[167]Wu FQ, Ma J, Ren GD, 2018c. Synchronization stability between initial-dependent oscillators with periodical and chaotic oscillation. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 19(12):889-903.

[168]Wu FQ, Ma J, Zhang G, 2019. A new neuron model under electromagnetic field. Applied Mathematics and Computation, 347:590-599.

[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.

[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.

[171]Xu Q, Song Z, Bao H, et al., 2018. Two-neuron-based non-autonomous memristive Hopfield neural network: numerical analyses and hardware experiments. AEU-International Journal of Electronics and Communications, 96:66-74.

[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.

[173]Xu Y, Jia Y, Kirunda JB, et al., 2018a. Dynamic behaviors in coupled neuron system with the excitatory and inhibitory autapse under electromagnetic induction. Complexity, 2018:3012743.

[174]Xu Y, Jia Y, Ge MY, et al., 2018b. Effects of ion channel blocks on electrical activity of stochastic Hodgkin–Huxley neural network under electromagnetic induction. Neurocomputing, 283:196-204.

[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.

[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.

[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.

[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.

[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.

[180]Yuste R, Bonhoeffer T, 2001. Morphological changes in dendritic spines associated with long-term synaptic plasticity. Annual Review of Neuroscience, 24:1071-1089.

[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.

[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.

[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.

[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.

[185]https://doi.org/10.14736/kyb-2018-4-0648

[186]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.

[187]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.

[188]Zhao ZG, Gu HG, 2017. Transitions between classes of neuronal excitability and bifurcations induced by autapse. Scientific Reports, 7(1):6760.

[189]Zheng HW, Wang RB, Qu JY, 2016. Effect of different glucose supply conditions on neuronal energy metabolism. Cognitive Neurodynamics, 10(6):563-571.

[190]Zonta M, Angulo MC, Gobbo S, et al., 2003. Neuron-to-astrocyte signaling is central to the dynamic control of brain microcirculation. Nature Neuroscience, 6(1):43-50.

[191]Zucker RS, 1989. Short-term synaptic plasticity. Annual Review of Neuroscience, 12:13-31.

[192]Zucker RS, Regehr WG, 2002. Short-term synaptic plasticity. Annual Review of Physiology, 64:355-405.