Abstract
Using the improved memristive Izhikevich neuron model, the effects of autaptic connection as well as electromagnetic induction are studied on the dynamical behavior of neuronal spiking. Using bifurcation analysis for membrane potentials, the effects of autaptic and electromagnetic parameters on the mode transition in electrical activities of the neuron model are investigated. Furthermore, white Gaussian noise is considered in the neuron model, to evaluate the effect of electromagnetic disturbance on the firing pattern of the neuron using the coefficient of variation. The bifurcation diagram versus autaptic conductance and time delay has been extensively studied. The results show that the effects of autaptic connection as well as electromagnetic induction on the spiking behavior of neurons can be well demonstrated by using the Izhikevich model. The electrical activities of the Izhikevich neuron model become more complex when the effects of autaptic connection and electromagnetic induction are considered in the neuron model. Using the Izhikevich neuron model, the high variety of spiking/bursting patterns is represented in the bifurcation diagram of inter-spike interval versus autaptic or electromagnetic parameters. Noise can have distinct effects on the spiking activity of the neuron, for the subthreshold input current, increasing the intensity of the electromagnetic noise increases the regularity of the neuron spiking, but for the suprathreshold input current, the regularity of spiking decreases with noise.
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References
Bartos, M., Vida, I., & Jonas, P. (2007). Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks. Nature Reviews Neuroscience, 8, 45–56. https://doi.org/10.1038/nrn2044
Bekkers, J. M. (2003). Synaptic transmission: Functional autapses in the cortex. Current Biology, 13, R433–R435. https://doi.org/10.1016/S0960-9822(03)00363-4
Bennett, M. V., & Zukin, R. S. (2004). Electrical coupling and neuronal synchronization in the mammalian brain. Neuron, 41, 495–511. https://doi.org/10.1016/S0896-6273(04)00043-1
Casado, J. M. (2003). Synchronization of two Hodgkin-Huxley neurons due to internal noise. Physics Letters A, 310, 400–406. https://doi.org/10.1016/S0375-9601(03)00387-6
Flight, M. H. (2009). Exerting self-control for persistence. Nature Reviews Neuroscience, 10, 316–316. https://doi.org/10.1038/nrn2637
Guo, D., Wu, S., Chen, M., Perc, M., Zhang, Y., Ma, J., Cui, Y., Xu, P., Xia, Y., & Yao, D. (2016). Regulation of irregular neuronal firing by autaptic transmission. Scientific Reports, 6, 1–14. https://doi.org/10.1038/srep26096
Hashemi, M., Valizadeh, A., & Azizi, Y. (2012). Effect of duration of synaptic activity on spike rate of a Hodgkin-Huxley neuron with delayed feedback. Physical Review E, 85, 021917. https://doi.org/10.1103/PhysRevE.85.021917
Herrmann, C. S., & Klaus, A. (2004). Autapse turns neuron into oscillator. International Journal of Bifurcation and Chaos, 14(02), 623–633. https://doi.org/10.1142/S0218127404009338
Hindmarsh, J. L., & Rose, R. M. (1984). A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal society of London Series B Biological sciences, 221, 87–102. https://doi.org/10.1098/rspb.1984.0024
Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117, 500–544. https://doi.org/10.1113/jphysiol.1952.sp004764
Ikeda, K., & Bekkers, J. M. (2006). Autapses. Current Biology, 16, R308.
Izhikevich, E. M. (2000). Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos, 10, 1171–1266. https://doi.org/10.1142/S0218127400000840
Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14, 1569–1572. https://doi.org/10.1109/TNN.2003.820440
Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons. IEEE Transactions on Neural Networks, 15, 1063–1070. https://doi.org/10.1109/TNN.2004.832719
Kandel, E. R., Schwartz, J. H., Jessell, T. M., Siegelbaum, S., Hudspeth, A. J., & Mack, S. (2000). Principles of neural science (4th ed.). McGraw-hill.
Li, Y., Gu, H., & Ding, X. (2019). Bifurcations of enhanced neuronal bursting activities induced by the negative current mediated by inhibitory autapse. Nonlinear Dynamics, 97, 2091–2105. https://doi.org/10.1007/s11071-019-05106-2
Li, Y., Schmid, G., Hänggi, P., & Schimansky-Geier, L. (2010). Spontaneous spiking in an autaptic Hodgkin-Huxley setup. Physical Review E, 82, 061907. https://doi.org/10.1103/PhysRevE.82.061907
Lu, L., Kirunda, J. B., Xu, Y., Kang, W., Ye, R., Zhan, X., & Jia, Y. (2018). Effects of temperature and electromagnetic induction on action potential of Hodgkin-Huxley model. The European Physical Journal Special Topics, 227, 767–776. https://doi.org/10.1140/epjst/e2018-700140-1
Lv, M., Wang, C., Ren, G., Ma, J., & Song, X. (2016). Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dynamics, 85, 1479–1490. https://doi.org/10.1007/s11071-016-2773-6
Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35, 193–213. https://doi.org/10.1016/S0006-3495(81)84782-0
Ostojic, S., Brunel, N., & Hakim, V. (2009). How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. Journal of Neuroscience, 29, 10234–10253. https://doi.org/10.1523/JNEUROSCI.1275-09.2009
Rowat, P. F., & Elson, R. C. (2004). State-dependent effects of Na channel noise on neuronal burst generation. Journal of Computational Neuroscience, 16, 87–112. https://doi.org/10.1023/B:JCNS.0000014104.08299.8b
Rocsoreanu, C., Georgescu, A., & Giurgiteanu, N. (2012). The FitzHugh-Nagumo model: bifurcation and dynamics (10th ed.). Springer Science & Business Media.
Seung, H. S., Lee, D. D., Reis, B. Y., & Tank, D. W. (2000). The autapse: A simple illustration of short-term analog memory storage by tuned synaptic feedback. Journal of Computational Neuroscience, 9, 171–185. https://doi.org/10.1023/A:1008971908649
Wang, G., Wu, Y., Xiao, F., Ye, Z., & Jia, Y. (2022). Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction. Physica a: Statistical Mechanics and Its Applications, 598, 127274. https://doi.org/10.1016/j.physa.2022.127274
Wang, H., Ma, J., Chen, Y., & Chen, Y. (2014). Effect of an autapse on the firing pattern transition in a bursting neuron. Communications in Nonlinear Science and Numerical Simulation, 19, 3242–3254. https://doi.org/10.1016/j.cnsns.2014.02.018
Xu, Y., Ying, H., Jia, Y., Ma, J., & Hayat, T. (2017). Autaptic regulation of electrical activities in neuron under electromagnetic induction. Scientific Reports, 7, 1–12. https://doi.org/10.1038/srep43452
Yang, X., Yu, Y., & Sun, Z. (2017). Autapse-induced multiple stochastic resonances in a modular neuronal network. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27, 083117. https://doi.org/10.1063/1.4999100
Yilmaz, E., Ozer, M., Baysal, V., & Perc, M. (2016). Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Scientific Reports, 6, 1–14. https://doi.org/10.1038/srep30914
Zhan, F., & Liu, S. (2017). Response of electrical activity in an improved neuron model under electromagnetic radiation and noise. Frontiers in Computational Neuroscience, 11, 107. https://doi.org/10.3389/fncom.2017.00107
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Feali, M., Hamidi, A. Dynamical response of Autaptic Izhikevich Neuron disturbed by Gaussian white noise. J Comput Neurosci 51, 59–69 (2023). https://doi.org/10.1007/s10827-022-00832-w
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DOI: https://doi.org/10.1007/s10827-022-00832-w