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Abstract: Biological neurons can receive inputs and capture a variety of external stimuli, which can be encoded and transmitted as different electric signals. Thus, the membrane potential is adjusted to activate the appropriate firing modes. Indeed, reliable neuron models should take intrinsic biophysical effects and functional encoding into consideration. One fascinating and important question is the physical mechanism for the transcription of external signals. External signals can be transmitted as a transmembrane current or a signal voltage for generating action potentials. We present a photosensitive neuron model to estimate the nonlinear encoding and responses of neurons driven by external optical signals. In the model, a photocell (phototube) is used to activate a simple FitzHugh-Nagumo (FHN) neuron, and then external optical signals (illumination) are imposed to excite the photocell for generating a time-varying current/voltage source. The photocell-coupled FHN neuron can therefore capture and encode external optical signals, similar to artificial eyes. We also present detailed bifurcation analysis for estimating the mode transition and firing pattern selection of neuronal electrical activities. The sampled time series can reproduce the main characteristics of biological neurons (quiescent, spiking, bursting, and even chaotic behaviors) by activating the photocell in the neural circuit. These results could be helpful in giving possible guidance for studying neurodynamics and applying neural circuits to detect optical signals.

一类新的光电神经元模型及其动力学

[1]Agostini P, Petite G, 1988. Photoelectric effect under strong irradiation. Contemp Phys, 29(1):57-77.

[2]Bao B, Yang Q, Zhu L, et al., 2019. Chaotic bursting dynamics and coexisting multistable firing patterns in 3D autonomous Morris-Lecar model and microcontroller-based validations. Int J Bifurc Chaos, 29(10):1950134.

[3]Bao H, Wang N, Wu HG, et al., 2019. Bi-stability in an improved memristor-based third-order Wien-bridge oscillator. IETE Techn Rev, 36(2):109-116.

[4]Batista CAS, Viana RL, Ferrari FAS, et al., 2013. Control of bursting synchronization in networks of Hodgkin-Huxley-type neurons with chemical synapses. Phys Rev E, 87(4):042713.

[5]Bera BK, Ghosh D, Lakshmanan M, 2016. Chimera states in bursting neurons. Phys Rev E, 93(1):012205.

[6]Bera BK, Rakshit S, Ghosh D, et al., 2019. Spike chimera states and firing regularities in neuronal hypernetworks. Chaos, 29(5):053115.

[7]Binczak S, Jacquir S, Bilbault JM, et al., 2006. Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability. Neur Networks, 19(5):684-693.

[8]Brust D, 1965. Band-theoretic model for the photoelectric effect in silicon. Phys Rev, 139(2A):A489.

[9]Cubero D, Baltanás JP, Casado-Pascual J, 2006. High- frequency effects in the FitzHugh-Nagumo neuron model. Phys Rev E, 73(6):061102.

[10]Duan LX, Cao QY, Wang ZJ, et al., 2018. Dynamics of neurons in the pre-Bötzinger complex under magnetic flow effect. Nonl Dynam, 94(3):1961-1971.

[11]Erokhin V, Berzina T, Camorani P, et al., 2011. Material memristive device circuits with synaptic plasticity: learning and memory. BioNanoScience, 1(1-2):24-30.

[12]Etémé AS, Tabi CB, Mohamadou A, et al., 2019. Elimination of spiral waves in a two-dimensional Hindmarsh-Rose neural network under long-range interaction effect and frequency excitation. Phys A, 533:122037.

[13]Fitzhugh R, 1961. Impulses and physiological states in theoretical models of nerve membrane. Biophys J, 1(6):445-466.

[14]Gaiko VA, 2011. Multiple limit cycle bifurcations of the FitzHugh-Nagumo neuronal model. Nonl Anal Theory Methods Appl, 74(18):7532-7542.

[15]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. Nonl Dynam, 91(1):515-523.

[16]Georges AT, 1995. Theory of the multiphoton photoelectric effect: a stepwise excitation process. Phys Rev B, 51(19): 13735-13738.

[17]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. Nonl Dynam, 81(4):2107-2126.

[18]Hagell P, Piccini P, Björklund A, et al., 2002. Dyskinesias following neural transplantation in Parkinson’s disease. Nat Neurosci, 5(7):627-628.

[19]Haghiri S, Ahmadi A, Saif M, 2016. VLSI implementable neuron-astrocyte control mechanism. Neurocomputing, 214:280-296.

[20]Han XJ, Bi QS, Zhang C, et al., 2014. Study of mixed-mode oscillations in a parametrically excited van der Pol system. Nonl Dynam, 77(4):1285-1296.

[21]Han XJ, Bi QS, Ji P, et al., 2015. Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies. Phys Rev E, 92(1):012911.

[22]Han XJ, Bi QS, Kurths J, 2018. Route to bursting via pulse-shaped explosion. Phys Rev E, 98(1):010201(R).

[23]Hauschildt B, Janson NB, Balanov A, et al., 2006. Noise- induced cooperative dynamics and its control in coupled neuron models. Phys Rev E, 74(5):051906.

[24]Hu XY, Liu CX, 2019. Dynamic property analysis and circuit implementation of simplified memristive Hodgkin-Huxley neuron model. Nonl Dynam, 97(2):1721-1733.

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

[26]Jia B, Wu YC, He D, et al., 2018. Dynamics of transitions from anti-phase to multiple in-phase synchronizations in inhibitory coupled bursting neurons. Nonl Dynam, 93(3): 1599-1618.

[27]Keener JP, 1983. Analog circuitry for the van der Pol and FitzHugh-Nagumo equations. IEEE Trans Syst Man Cybern, SMC-13(5):1010-1014.

[28]Kyprianidis IM, Papachristou V, Stouboulos IN, et al., 2012. Dynamics of coupled chaotic Bonhoeffer-van der Pol oscillators. WSEAS Trans Syst, 11(9):516-526.

[29]Liu ZL, Ma J, Zhang G, et al., 2019. Synchronization control between two Chua’s circuits via capacitive coupling. Appl Math Comput, 360:94-106.

[30]Lv M, Ma J, Yao YG, et al., 2019. Synchronization and wave propagation in neuronal network under field coupling. Sci China Technol Sci, 62(3):448-457.

[31]Ma J, Zhang G, Hayat T, et al., 2019a. Model electrical activity of neuron under electric field. Nonl Dynam, 95(2):1585-1598.

[32]Ma J, Yang ZQ, Yang LJ, et al., 2019b. A physical view of computational neurodynamics. J Zhejiang Univ-Sci A (Appl Phys & Eng), 20(9):639-659.

[33]Ma YQ, Wang ZR, Yu SY, et al., 2018. A novel spiking neural network of receptive field encoding with groups of neurons decision. Front Inform Technol Electron Eng, 19(1):139-150.

[34]Meng FQ, Zeng XQ, Wang ZL, 2019. Dynamical behavior and synchronization in time-delay fractional-order coupled neurons under electromagnetic radiation. Nonl Dynam, 95(2):1615-1625.

[35]Mondal A, Upadhyay RK, 2018. Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking. Nonl Dynam, 91(2):1275-1288.

[36]Mostaghimi S, Nazarimehr F, Jafari S, et al., 2019. Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow. Appl Math Comput, 348:42-56.

[37]Nair MV, Muller LK, Indiveri G, 2017. A differential memristive synapse circuit for on-line learning in neuromorphic computing systems. Nano Fut, 1(3):035003.

[38]Nazari S, Amiri M, Faez K, et al., 2015. Multiplier-less digital implementation of neuron-astrocyte signalling on FPGA. Neurocomputing, 164:281-292.

[39]Pankratova EV, Kalyakulina AI, Stasenko SV, et al., 2019. Neuronal synchronization enhanced by neuron-astrocyte interaction. Nonl Dynam, 97(1):647-662.

[40]Park S, Chu M, Kim J, et al., 2015. Electronic system with memristive synapses for pattern recognition. Sci Rep, 5(1):10123.

[41]Pham VT, Jafari S, Vaidyanathan S, et al., 2016. A novel memristive neural network with hidden attractors and its circuitry implementation. Sci China Technol Sci, 59(3):358-363.

[42]Postnov DE, Koreshkov RN, Brazhe NA, et al., 2009. Dynamical patterns of calcium signaling in a functional model of neuron-astrocyte networks. J Biol Phys, 35(4):425-445.

[43]Rajagopal K, Nazarimehr F, Karthikeyan A, et al., 2019. Dynamics of a neuron exposed to integer- and fractional-order discontinuous external magnetic flux. Front Inform Technol Electron Eng, 20(4):584-590.

[44]Rakshit S, Bera BK, Ghosh D, et al., 2018a. Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks. Phys Rev E, 97(5): 052304.

[45]Rakshit S, Bera BK, Ghosh D, 2018b. Synchronization in a temporal multiplex neuronal hypernetwork. Phys Rev E, 98(3):032305.

[46]Rakshit S, Ray A, Bera BK, et al., 2018c. Synchronization and firing patterns of coupled Rulkov neuronal map. Nonl Dynam, 94(2):785-805.

[47]Richardson MJE, Swarbrick R, 2010. Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise. Phys Rev Lett, 105(17):178102.

[48]Rostami Z, Pham VT, Jafari S, et al., 2018. Taking control of initiated propagating wave in a neuronal network using magnetic radiation. Appl Math Comput, 338:141-151.

[49]Seifert G, Steinhäuser C, 2013. Neuron-astrocyte signaling and epilepsy. Exp Neurol, 244:4-10.

[50]Takembo CN, Mvogo A, Fouda HPE, et al., 2019a. Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network. Nonl Dynam, 95(2):1067-1078.

[51]Takembo CN, Mvogo A, Fouda HPE, et al., 2019b. Wave pattern stability of neurons coupled by memristive electromagnetic induction. Nonl Dynam, 96(2):1083-1093.

[52]Tang J, Zhang J, Ma J, et al., 2019. Noise and delay sustained chimera state in small world neuronal network. Sci China Technol Sci, 62(7):1134-1140.

[53]Upadhyay RK, Mondal A, Teka WW, 2017. Mixed mode oscillations and synchronous activity in noise induced modified Morris-Lecar neural system. Int J Bifurc Chaos, 27(5):1730019.

[54]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. Phys A, 486:386-396.

[55]Wang CN, Lv M, Alsaedi A, et al., 2017. Synchronization stability and pattern selection in a memristive neuronal network. Chaos, 27(11):113108.

[56]Wang YH, Xu XY, Zhu YT, et al., 2019. Neural energy mechanism and neurodynamics of memory transformation. Nonl Dynam, 97(1):697-714.

[57]Wu FQ, Wang CN, Xu Y, et al., 2016. Model of electrical activity in cardiac tissue under electromagnetic induction. Sci Rep, 6(1):28.

[58]Wu FQ, Wang CN, Jin WY, et al., 2017. Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Phys A, 469:81-88.

[59]Wu FQ, Ma J, Zhang G, 2019. A new neuron model under electromagnetic field. Appl Math Comput, 347:590-599.

[60]Xu F, Zhang JQ, Fang TT, et al., 2018. Synchronous dynamics in neural system coupled with memristive synapse. Nonl Dynam, 92(3):1395-1402.

[61]Xu Q, Zhang QL, Qian H, et al., 2018. Crisis-induced coexisting multiple attractors in a second-order nonautonomous memristive diode bridge-based circuit. Int J Circ Theor Appl, 46(10):1917-1927.

[62]Xu Y, Jia Y, Ma J, et al., 2018a. Collective responses in electrical activities of neurons under field coupling. Sci Rep, 8(1):1349.

[63]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.

[64]Xu Y, Jia Y, Wang HW, et al., 2019. Spiking activities in chain neural network driven by channel noise with field coupling. Nonl Dynam, 95(4):3237-3247.

[65]Yao Z, Ma J, Yao YG, et al., 2019. Synchronization realization between two nonlinear circuits via an induction coil coupling. Nonl Dynam, 96(1):205-217.

[66]Ye WJ, Mai WD, Hu GW, 2018. Effects of the electromagnetic radiation on cognitive performance: a model study. Nonl Dynam, 93(4):2473-2485.

[67]Yu DS, Zheng CY, Iu HHC, et al., 2017. A new circuit for emulating memristors using inductive coupling. IEEE Access, 5:1284-1295.

[68]Yu Y, Zhang C, Han XJ, 2017. Routes to bursting in active control system with multiple time delays. Nonl Dynam, 88(3):2241-2254.

[69]Zhang YZ, Liu Z, Wu HG, et al., 2019a. Dimensionality reduction analysis for detecting initial effects on synchronization of memristor-coupled system. IEEE Access, 7: 109689-109698.

[70]Zhang YZ, Liu Z, Wu HG, et al., 2019b. Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis. Chaos Sol Fract, 127:354-363.