Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction
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摘要
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.
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.
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.
引文
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2 Zhang P,Adams U,Yuan Z Q.Re-mention of an old neurodegenerative disease:Alzheimer’s disease.Chin Sci Bull,2013,58:1731-1736
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4 Fitzhugh R.Impulses and physiological states in theoretical models of nerve membrane.Biophys J,1961,1:445-466
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7 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
8 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
9 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
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11 Nordenfelt A,Used J,Sanjuán M A F.Bursting frequency versus phase synchronization in time-delayed neuron networks.Phys Rev E,2013,87:052903
12 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
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14 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
15 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
16 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
17 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
18 Izhikevich E M.Which model to use for cortical spiking neurons?IEEE Trans Neural Netw,2004,15:1063-1070
19 Gu H G,Chen S G.Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker.Sci China Tech Sci,2014,57:864-871
20 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
21 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
22 Wang H T,Chen Y.Firing dynamics of an autaptic neuron.Chin Phys B,2015,24:128709
23 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
24 Wang Z H,Wang Q Y.Effect of the coordinated reset stimulations on controlling absence seizure.Sci China Tech Sci,2017,60:985-994
25 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
26 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
27 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
28 Yan C.A Neuron Model Based on Hamilton Principle and Energy Coding.Berlin,Heidelberg:Springer,2012.395-401
29 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
30 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
31 Sarasola C,Torrealdea F J,D'Anjou A,et al.Energy balance in feedback synchronization of chaotic systems.Phys Rev E,2004,69:011606
32 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
33 Carpenter C J.Electromagnetic induction in terms of the Maxwell force instead of magnetic flux.IEE Proc-Sci Measurement Tech,1999,146:182-193
34 Bao B C,Liu Z,Xu J P.Steady periodic memristor oscillator with transient chaotic behaviours.Electron Lett,2010,46:228
35 Muthuswamy B.Implementing memristor based chaotic circuits.Int JBifurcation Chaos,2010,20:1335-1350
36 Harris J J,Jolivet R,Attwell D.Synaptic energy use and supply.Neuron,2012,75:762-777
37 Wang R,Zhang Z,Chen G.Energy coding and energy functions for local activities of the brain.Neurocomputing,2009,73:139-150
38 Torrealdea F J,Sarasola C,D'Anjou A,et al.Energy efficiency of information transmission by electrically coupled neurons.Biosystems,2009,97:60-71
39 Song X L,Jin W Y,Ma J.Energy dependence on the electric activities of a neuron.Chin Phys B,2015,24:128710
2 Zhang P,Adams U,Yuan Z Q.Re-mention of an old neurodegenerative disease:Alzheimer’s disease.Chin Sci Bull,2013,58:1731-1736
3 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
4 Fitzhugh R.Impulses and physiological states in theoretical models of nerve membrane.Biophys J,1961,1:445-466
5 Morris C,Lecar H.Voltage oscillations in the barnacle giant muscle fiber.Biophys J,1981,35:193-213
6 Hindmarsh J L,Rose R M.A model of the nerve impulse using two first-order differential equations.Nature,1982,296:162-164
7 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
8 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
9 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
10 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
11 Nordenfelt A,Used J,Sanjuán M A F.Bursting frequency versus phase synchronization in time-delayed neuron networks.Phys Rev E,2013,87:052903
12 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
13 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
14 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
15 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
16 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
17 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
18 Izhikevich E M.Which model to use for cortical spiking neurons?IEEE Trans Neural Netw,2004,15:1063-1070
19 Gu H G,Chen S G.Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker.Sci China Tech Sci,2014,57:864-871
20 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
21 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
22 Wang H T,Chen Y.Firing dynamics of an autaptic neuron.Chin Phys B,2015,24:128709
23 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
24 Wang Z H,Wang Q Y.Effect of the coordinated reset stimulations on controlling absence seizure.Sci China Tech Sci,2017,60:985-994
25 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
26 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
27 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
28 Yan C.A Neuron Model Based on Hamilton Principle and Energy Coding.Berlin,Heidelberg:Springer,2012.395-401
29 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
30 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
31 Sarasola C,Torrealdea F J,D'Anjou A,et al.Energy balance in feedback synchronization of chaotic systems.Phys Rev E,2004,69:011606
32 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
33 Carpenter C J.Electromagnetic induction in terms of the Maxwell force instead of magnetic flux.IEE Proc-Sci Measurement Tech,1999,146:182-193
34 Bao B C,Liu Z,Xu J P.Steady periodic memristor oscillator with transient chaotic behaviours.Electron Lett,2010,46:228
35 Muthuswamy B.Implementing memristor based chaotic circuits.Int JBifurcation Chaos,2010,20:1335-1350
36 Harris J J,Jolivet R,Attwell D.Synaptic energy use and supply.Neuron,2012,75:762-777
37 Wang R,Zhang Z,Chen G.Energy coding and energy functions for local activities of the brain.Neurocomputing,2009,73:139-150
38 Torrealdea F J,Sarasola C,D'Anjou A,et al.Energy efficiency of information transmission by electrically coupled neurons.Biosystems,2009,97:60-71
39 Song X L,Jin W Y,Ma J.Energy dependence on the electric activities of a neuron.Chin Phys B,2015,24:128710