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Han Fang, Wang Qingyun. Research advances and some thoughts on neurodynamics. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-9 doi: 10.6052/0459-1879-22-404
Citation: Han Fang, Wang Qingyun. Research advances and some thoughts on neurodynamics. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-9 doi: 10.6052/0459-1879-22-404


doi: 10.6052/0459-1879-22-404
  • Received Date: 2022-08-31
  • Accepted Date: 2022-10-09
  • Available Online: 2022-10-10
  • Neurodynamics is a foundational branch of dynamics and control, which belongs to the international frontier of the interdisciplinary field of mechanics, brain science and intelligence science. Based on the basic theories and methods of dynamics and control, the study of neurodynamics mainly focuses on establishing reasonable models to explore the mechanisms of electrophysiological dynamic behaviors of nervous system and brain cognitive functions. In recent years, scholars at home and abroad have obtained remarkable achievements in the foundational research of neurodynamics, including the in-depth study of the dynamical behavior of neurons and neural networks, the modeling and analysis of different functional structures of the brain, and the network dynamics modeling and control of brain regions associated with nervous disease. In this paper, we firstly overviewed elaborately the recent advancements in the field of neurodynamics. Especially, development history for advancement of neural modeling is exhibited. Then, by analyzing the research outcomes of biological neural networks and their dynamics, some thoughts and prospects for future research are put forward. It is expected that neurodynamics will contribute to the breakthroughs of the theories and methods of brain-like intelligence and intelligent equipment with strong interpretability and generalization ability, and finally their applications in major engineering projects.


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  • [1]
    Freeman WJ. Mesoscopic neurodynamics: From neuron to brain. Journal of Physiology-Paris, 2000, 94(5-6): 303-322 doi: 10.1016/S0928-4257(00)01090-1
    Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 1952, 117(4): 500-544 doi: 10.1113/jphysiol.1952.sp004764
    Fitzhugh R. Mathematical models of threshold phenomena in the nerve membrane. Bulletin of Mathematical Biology, 1955, 17(4): 257-278
    Hindmarsh JL, Rose RM. A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society B: Biological Sciences, 1984, 221(1222): 87-102
    Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 1981, 35(1): 193-213 doi: 10.1016/S0006-3495(81)84782-0
    Chay TR. Chaos in a three-variable model of an excitable cell. Physica D: Nonlinear Phenomena, 1985, 16(2): 233-242 doi: 10.1016/0167-2789(85)90060-0
    Izhikevich EM. Simple model of spiking neurons. IEEE Transactions on Neural Networks, 2015, 14: 1569-1572
    Lapicque, L. Recherches quantitatives sur l’excitation ´electrique des nerfs trait´ee comme une polarisation. J. Physiol. Pathol. Gen., 1907, 9: 620-635
    Rinzel J. Bursting oscillations in an excitable membrane model. Springer Berlin Heidelberg, 1985, 47(3): 357-366
    Izhikevich EM. Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos, 2012, 10(6): 1171-1266
    王青云, 陆启韶. 兴奋性化学突触耦合的神经元的同步. 动力学与控制学报, 2020, 18(1): 1-5 (Wang Rubin. Research advances in neurodynamics. Journal of Dynamics and Control, 2020, 18(1): 1-5 (in Chinese) doi: 10.6052/1672-6553-2020-013
    王海侠, 陆启韶, 郑艳红. 神经元模型的复杂动力学: 分岔与编码. 动力学与控制学报, 2009, 7(4): 293-296 (Wang Haixia, Lu Qishao, Zheng Yanhong. Complex dynamics of the neuronal model: bifurcation and encoding. Journal of Dynamics and Control, 2009, 7(4): 293-296 (in Chinese)
    Canavier CC. Reciprocal excitatory synapses convert pacemaker-like Firing into burst firing in a simple model of coupled neurons. Neurocomputing, 2000, 32: 331-338
    Booth V, Bose A. Transitions between different synchronous firing modes using synaptic depression. Neurocomputing, 2002, 44: 61-67
    Casado JM. Synchronization of two Hodgkin–Huxley neurons due to internal noise. Physics Letters A, 2003, 310(5-6): 400-406 doi: 10.1016/S0375-9601(03)00387-6
    Wang Q, Perc M, Duan Z, et al. Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2009, 80(2): 026206
    Wang Q, Duan Z, Perc M, et al. Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability. Europhysics Letters, 2008, 83(5): 50008 doi: 10.1209/0295-5075/83/50008
    Wu J, Ma S. Coherence resonance of the spiking regularity in a neuron under electromagnetic radiation. Nonlinear Dynamics, 2019, 96: 1895-1908 doi: 10.1007/s11071-019-04892-z
    Lü M, Ma J. Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing, 2016, 205: 375-381
    Dayan P, Abbott LF. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press, 2001
    Abbott LF. Theoretical neuroscience rising. Neuron, 2008, 60(3): 489-495 doi: 10.1016/j.neuron.2008.10.019
    Olshausen BA, Field DJ. Sparse coding of sensory inputs. Current Opinion in Neurobiology, 2004, 14(4): 481-487 doi: 10.1016/j.conb.2004.07.007
    Chaudhuri R, Fiete I. Computational principles of memory. Nature Neuroscience, 2016, 19(3): 394-403
    Wang XJ. Decision making in recurrent neuronal circuits. Neuron, 2008, 60(2): 215-234 doi: 10.1016/j.neuron.2008.09.034
    Diedrichsen J, Shadmehr R, Ivry RB. The coordination of movement:optimal feedback control and beyond. Trends in Cognitive Sciences, 2010, 14(1): 31-39
    Beck C, Neumann H. Interactions of motion and form in visual cortex-A neural model. J. Physiol. Paris, 2010, 104(1-2): 61-70 doi: 10.1016/j.jphysparis.2009.11.005
    Pinotsis DA, Schwarzkopf DS, Litvak V, et al. Dynamic causal modelling of lateral interactions in the visual cortex. NeuroImage, 2012, 66: 563-576
    Guzman SJ. Synaptic mechanisms of pattern completion in the hippocampal CA3 network. Science, 2016, 353(6304): 1117-1123
    宋健, 刘深泉, 臧杰. 基于基底神经节机理的行为决策模型. 动力学与控制学报, 2020, 18(6): 1-31 (Song Jian, Liu Shenquan, Zang Jie. Behavior decision-making model based on basal ganglia mechanism. Journal of Dynamics and Control, 2020, 18(6): 1-31 (in Chinese) doi: 10.1126/science.aaf1836
    Humphries MD, Stewart RD, Gurney KN. A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. The Journal of Neuroscience, 2006, 26(50): 12921-12942 doi: 10.1523/JNEUROSCI.3486-06.2006
    Gurney K, Prescott TJ, Redgrave P. A computational model of action selection in the basal ganglia. I: A new functional anatomy. Biological Cybernetics, 2001, 84(6): 401-410
    Dura-Bernal S, Zhou X, Neymotin SA, et al. Cortical spiking network interfaced with virtual musculoskeletal arm and robotic arm. Frontiers in Neurorobotics, 2015, 9: 13
    Taegyo K, Hamade KC, Dmitry T, et al. Reward based motor adaptation mediated by basal ganglia. Frontiers in Computational Neuroscience, 2017, 11: 19
    Todorov DI, Capps RA, Barnett WH, et al. The interplay between cerebellum and basal ganglia in motor adaptation: A modeling study. PLoS ONE, 2019, 14(4): e0214926 doi: 10.1371/journal.pone.0214926
    Rabinovich MI, Muezzinoglu MK. Nonlinear dynamics of the brain: emotion and cognition. Physics-Uspekhi, 2010, 53(4): 357-372 doi: 10.3367/UFNe.0180.201004b.0371
    Kriegeskorte N. Deep neural networks: A new framework for modeling biological vision and brain information processing. Annual Review of Vision Science, 2015, 1(1): 417
    王如彬, 王毅泓, 徐旭颖等. 认知神经科学中蕴藏的力学思想与应用. 力学进展, 2020, 50(1): 450-505 (Wang Rubin, Wang Yihong, Xu Xuying, et al. Mechanical thoughtsand applications in cognitive neuroscience. Advances in Mechanics, 2020, 50(1): 450-505 (in Chinese) doi: 10.1146/annurev-vision-082114-035447
    彭俊, 王如彬, 王毅泓. 大脑血液动力学现象中的能量编码. 力学学报, 2019, 51(4): 1202-1209 (Peng Jun, Wang Rubin, Wang Yihong. Energy coding of hemodynamic phenomena in the brain. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1202-1209 (in Chinese)
    Wendling F, Bartolomei F, Bellanger JJ, et al. Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. European Journal of Neuroscience, 2002, 15: 1499-1508 doi: 10.1046/j.1460-9568.2002.01985.x
    Taylor PN, Baier G. A spatially extended model for macroscopic spike-wave-discharges. Journal of Computational Neuroscience, 2011, 31(3): 679-684
    韩芳, 樊登贵, 张丽媛等. 神经系统疾病与认知动力学(Ⅰ): 癫痫发作的动力学与控制. 力学进展, 2022, 52(2): 339-396 (Han Fang, Fan Denggui, Zhang Liyuan, et al. Neurological disease and cognitive dynamics (I): Dynamics and control of epileptic seizures. Advances in Mechanics, 2022, 52(2): 339-396 (in Chinese) doi: 10.1007/s10827-011-0332-1
    Fan D, Wang Q, Matjaz P. Disinhibition-induced transitions between absence and tonic-clonic epileptic seizures. Scientific Reports, 2015, 5: 12618 doi: 10.1038/srep12618
    Wang Z, Wang Q. Eliminating absence seizures through the deep brain stimulation to thalamus reticular nucleus. Frontiers in Computational Neuroscience, 2017, 11: 22
    Zhang L, Wang Q, Baier G. Spontaneous transitions to focal-onset epileptic seizures: A dynamical study. Chaos, 2020, 30(10): 103114 doi: 10.1063/5.0021693
    Fan D, Liu S, Wang Q. Stimulus-induced epileptic spike-wave discharges in thalamocortical model with disinhibition. Scientific Reports, 2016, 6: 37703 doi: 10.1038/srep37703
    Yang C, Luan G, Liu Z, et al. Dynamical analysis of epileptic characteristics based on recurrence quantification of SEEG recordings. Physica A, 2019, 523: 507-515 doi: 10.1016/j.physa.2019.02.017
    Terman D, Rubin JE, Yew AC, et al. Activity patterns in a model for the subthalamopallidal network of the basal ganglia. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 2002, 22(7): 2963-2976 doi: 10.1523/JNEUROSCI.22-07-02963.2002
    Tass PA. Stochastic phase resetting of two coupled phase oscillators stimulated at different times. Physical Review E, 2003, 67(5): 05190
    Popovych OV, Tass PA. Multisite delayed feedback for electrical brain stimulation. Frontiers in Physiology, 2018, 9: 46 doi: 10.3389/fphys.2018.00046
    Yu Y, Hao Y, Wang Q. Model-based optimized phase-deviation deep brain stimulation for Parkinson's disease. Neural Networks, 2019, 122: 308-319
    Fan D, Wang Z, Wang Q. Optimal control of directional deep brain stimulation in the parkinsonian neuronal network. Communications in Nonlinear Science and Numerical Simulation, 2016, 36: 219-237 doi: 10.1016/j.cnsns.2015.12.005
    Fan D, Wang Q. Improving desynchronization of parkinsonian neuronal network via triplet-structure coordinated reset stimulation. Journal of Theoretical Biology, 2015, 370: 157-170 doi: 10.1016/j.jtbi.2015.01.040
    Zetterberg LH, Kristiansson L, Mossberg K. Performance of a model for a local neuron population. Biol. Cybern., 1978, 31(1): 15-26
    Traub RD, Knowles WD, Miles R, et al. Models of the cellular mechanism underlying propagation of epileptiform activity in the CA2-CA3 region of the hippocampal slice. Neuroscience, 1987, 21(2): 457-470 doi: 10.1016/0306-4522(87)90135-7
    Lytton WW, Sejnowski TJ. Computer model of ethosuximide's effect on a thalamic neuron. Ann. Neurol., 1992, 32(2): 131-139
    Destexhe A. Can GABAA conductances explain the fast oscillation frequency of absence seizures in rodents? European JournaL of Neuroscience, 1999, 11(6): 2175-2181
    Robinson PA, Rennie CJ, Rowe DL, et al. Neurophysical modeling of brain dynamics. Neuropsychopharmacology. 2003, Suppl. 1: S74-9
    Zhang L, Fan D, Wang Q. Transition dynamics of a dentate Gyrus-CA3 neuronal network during temporal lobe epilepsy. Frontiers in Computational Neuroscience, 2017, 11: 61 doi: 10.3389/fncom.2017.00061
    Albada S, Robinson PA. Mean-field modeling of the basal ganglia-thalamocortical system. I: Firing rates in healthy and parkinsonian states. Journal of Theoretical Biology, 2009, 257(4): 642-66361
    So RQ, Kent AR, Grill WM. Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study. Journal of Computational Neuroscience, 2012, 32(3): 499-519
    Kerr CC, van Albada SJ, Neymotin SA, et al. Cortical information flow in Parkinson’s disease: A composite network/field model. Frontiers in Computational Neuroscience, 2013, 7(39): 1-14
    Yu Y, Wang Q. Oscillation dynamics in an extended model of thalamic-basal ganglia. Nonlinear Dynamics, 2019, 98: 1065-1080 doi: 10.1007/s11071-019-05249-2
    Yu Y, Han F, Wang Q. Exploring phase-amplitude coupling from primary motor cortex-basal ganglia-thalamus network model. Neural Networks. 2022, 153: 130-141
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