Abstract
Energy supply and release play an important role in individual neuron and neural network. In this paper, the electrical activities and Hamilton energy of neuron are investigated when external mixed signals (i.e., the periodic stimulus current and the periodic electromagnetic field) are imposed on the neuron under the electromagnetic induction. As a result, the Hamilton energy is much dependent on the mode transition, the multiple electric activity modes and the numerical analysis of Hamilton energy are more complicated under various parameters. When the periodic high-low frequency electromagnetic radiation is imposed in neuron, it is found that the electrical activities are more complex, and the changing of energy is obvious. In addition, the response of electrical activity and Hamilton energy is much dependent on the changing of amplitude A, B when the external high-low frequency signal is imposed on the neuron, meanwhile, the energy of bursting state is lower than the one of spiking state. It can be used for investigation about the energy coding in the neuron even the neuron networks.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Puls I, Jonnakuty C, LaMonte B H, et al. Mutant dynactin in motor neuron disease. Nat Genet, 2003, 33: 455–456
Zhang P, Adams U, Yuan Z Q. Re-mention of an old neurodegenerative disease: Alzheimer’s disease. Chin Sci Bull, 2013, 58: 1731–1736
Hodgkin A L, Huxley A F. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol, 1952, 116: 449–472
Fitzhugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J, 1961, 1: 445–466
Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys J, 1981, 35: 193–213
Hindmarsh J L, Rose R M. A model of the nerve impulse using two first-order differential equations. Nature, 1982, 296: 162–164
Fan D G, Wang Q Y. Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays. Sci China Tech Sci, 2017, 60: 1019–1031
Ando H, Suetani H, Kurths J, et al. Chaotic phase synchronization in bursting-neuron models driven by a weak periodic force. Phys Rev E, 2012, 86: 016205
Yang L, Jia Y, Yi M. The effects of electrical coupling on the temporal coding of neural signal in noisy Hodgkin-Huxley neuron ensemble. In: 2010 Sixth International Conference on Natural Computation (ICNC). Yantai: IEEE, 2010. 819–823
Ma J, Qin H, Song X, et al. Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int J Mod Phys B, 2015, 29: 1450239
Nordenfelt A, Used J, Sanjuán M A F. Bursting frequency versus phase synchronization in time-delayed neuron networks. Phys Rev E, 2013, 87: 052903
Han Q K, Sun X Y, Yang X G, et al. External synchronization of two dynamical systems with uncertain parameters. Sci China Tech Sci, 2010, 53: 731–740
Qin H X, Ma J, Jin W Y, et al. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Tech Sci, 2014, 57: 936–946
Lu L, Jia Y, Liu W, et al. Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. Complexity, 2017, 2017: 7628537
Ge M, Jia Y, Xu Y, et al. Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn, 2018, 91: 515–523
Liao X, Li S, Chen G. Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain. Neural Netw, 2004, 17: 545–561
Xie Y, Kang Y M, Liu Y, et al. Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons. Sci China Tech Sci, 2014, 57: 914–922
Izhikevich E M. Which model to use for cortical spiking neurons? IEEE Trans Neural Netw, 2004, 15: 1063–1070
Gu H G, Chen S G. Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pa-cemaker. Sci China Tech Sci, 2014, 57: 864–871
Laflaquiere A, Masson S L, Dupeyron D, et al. Analog circuits emulating biological neurons in real-time experiments. In: Proceedings of 19th International Conference (IEEE/EMBS). Chicago, 1997. 2035–2038
Gu H, Pan B, Chen G, et al. Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dyn, 2014, 78: 391–407
Wang H T, Chen Y. Firing dynamics of an autaptic neuron. Chin Phys B, 2015, 24: 128709
Tang J, Zhang J, Ma J, et al. Astrocyte calcium wave induces seizurelike behavior in neuron network. Sci China Tech Sci, 2017, 60: 1011–1018
Wang Z H, Wang Q Y. Effect of the coordinated reset stimulations on controlling absence seizure. Sci China Tech Sci, 2017, 60: 985–994
Zhang H H, Zheng Y H, Su J Z, et al. Seizures dynamics in a neural field model of cortical-thalamic circuitry. Sci China Tech Sci, 2017, 60: 974–984
Li J J, Xie Y, Yu Y G, et al. A neglected GABAergic astrocyte: Calcium dynamics and involvement in seizure activity. Sci China Tech Sci, 2017, 60: 1003–1010
Guo D Q, Xia C, Wu S D, et al. Stochastic fluctuations of permittivity coupling regulate seizure dynamics in partial epilepsy. Sci China Tech Sci, 2017, 60: 995–1002
Yan C. A Neuron Model Based on Hamilton Principle and Energy Coding. Berlin, Heidelberg: Springer, 2012. 395–401
Nabi A, Mirzadeh M, Gibou F, et al. Minimum energy spike randomization for neurons. In: 2012 American Control Conference Fairmont Queen Elizabeth. Montreal: IEEE, 2012. 4751–4756
Ma J, Wu F, Jin W, et al. Calculation of Hamilton energy and control of dynamical systems with different types of attractors. Chaos, 2017, 27: 053108
Sarasola C, Torrealdea F J, D’Anjou A, et al. Energy balance in feedback synchronization of chaotic systems. Phys Rev E, 2004, 69: 011606
Lv M, Wang C, Ren G, et al. Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn, 2016, 85: 1479–1490
Carpenter C J. Electromagnetic induction in terms of the Maxwell force instead of magnetic flux. IEE Proc-Sci Measurement Tech, 1999, 146: 182–193
Bao B C, Liu Z, Xu J P. Steady periodic memristor oscillator with transient chaotic behaviours. Electron Lett, 2010, 46: 228
Muthuswamy B. Implementing memristor based chaotic circuits. Int J Bifurcation Chaos, 2010, 20: 1335–1350
Harris J J, Jolivet R, Attwell D. Synaptic energy use and supply. Neuron, 2012, 75: 762–777
Wang R, Zhang Z, Chen G. Energy coding and energy functions for local activities of the brain. Neurocomputing, 2009, 73: 139–150
Torrealdea F J, Sarasola C, D’Anjou A, et al. Energy efficiency of information transmission by electrically coupled neurons. Biosystems, 2009, 97: 60–71
Song X L, Jin W Y, Ma J. Energy dependence on the electric activities of a neuron. Chin Phys B, 2015, 24: 128710
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, L., Jia, Y., Xu, Y. et al. Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction. Sci. China Technol. Sci. 62, 427–440 (2019). https://doi.org/10.1007/s11431-017-9217-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-017-9217-x