Dynamic Characteristics of Fractional-order Photosensitive Neuron and Its Coupling Synchronization
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摘要: 神经元是神经系统的基本单位，神经元模型的准确性影响对其本质特征的分析和理解。该文研究了由分数阶电容和电感构成的分数阶光敏FitzHugh-Nagumo(FHN)神经元电路。利用分岔图、相轨迹图和时间序列图分析了分数阶光敏神经元模型的动力学特性。研究发现，随着分数阶阶次的降低，分数阶光敏神经元的活跃度增加。当选取不同参数时，神经元系统可以诱发不同的放电模式，如周期放电态、混沌放电态和尖峰放电态。此外，利用电突触耦合的方式连接两个分数阶光敏神经元。通过调整耦合强度，可以实现分数阶光敏神经元系统之间的相位同步和完全同步。最后，采用dSPACE验证了外部光信号对神经元兴奋性的调制作用。Abstract: Neurons are the basic unit of the nervous system, and the accuracy of neuron models affects the analysis and understanding of their essential properties. In this paper, a fractional-order photosensitive FitzHugh-Nagumo (FHN) neuron circuit constructed by fractional-order capacitor and inductor is investigated. The dynamics of the fractional-order photosensitive neuron model are analyzed using bifurcation diagrams, phase portraits, and time series diagrams. It was found that the activity of the fractional-order photosensitive neuron increased as the fractional-order decreased. When different system parameters are selected, the neuron system transitions between periodic and chaotic discharge states. The system can induce different discharge modes, such as periodic discharge states, chaotic discharge states, and spike discharge states. In addition, two fractional-order photosensitive neurons were connected using electrical synaptic coupling. Phase synchronization and complete synchronization between the fractional-order photosensitive neuron systems can be achieved by adjusting the coupling strength. Finally, the modulation effect of an external light signal on neuronal excitability was verified by dSPACE.
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Key words:
- Neurons /
- Photosensitive neuron /
- Fractional calculus /
- Synchronization
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[1] MA Jun, SONG Xinlin, JIN Wuyin, et al. Autapse-induced synchronization in a coupled neuronal network[J]. Chaos, Solitons & Fractals, 2015, 80: 31–38. doi: 10.1016/j.chaos.2015.02.005. [2] TORRES J J, ELICES I, and MARRO J. Efficient transmission of subthreshold signals in complex networks of spiking neurons[J]. PLoS One, 2015, 10(3): e0121156. doi: 10.1371/journal.pone.0121156. [3] BELYKH I, DE LANGE E, and HASLER M. Synchronization of bursting neurons: What matters in the network topology[J]. Physical Review Letters, 2005, 94(18): 188101. doi: 10.1103/PhysRevLett.94.188101. [4] WIG G S, SCHLAGGAR B L, and PETERSEN S E. Concepts and principles in the analysis of brain networks[J]. Annals of the New York Academy of Sciences, 2011, 1224(1): 126–146. doi: 10.1111/j.1749-6632.2010.05947.x. [5] IZHIKEVICH E M. Which model to use for cortical spiking neurons?[J]. IEEE Transactions on Neural Networks, 2004, 15(5): 1063–1070. doi: 10.1109/TNN.2004.832719. [6] OZER M and EKMEKCI N H. Effect of channel noise on the time-course of recovery from inactivation of sodium channels[J]. Physics Letters A, 2005, 338(2): 150–154. doi: 10.1016/j.physleta.2005.02.039. [7] HODGKIN A L and HUXLEY A F. A quantitative description of membrane current and its application to conduction and excitation in nerve[J]. The Journal of Physiology, 1952, 117(4): 500–544. doi: 10.1113/jphysiol.1952.sp004764. [8] FITZHUGH R. Impulses and physiological states in theoretical models of nerve membrane[J]. Biophysical Journal, 1961, 1(6): 445–466. doi: 10.1016/S0006-3495(61)86902-6. [9] HINDMARSH J L and ROSE R M. A model of neuronal bursting using three coupled first order differential equations[J]. Proceedings of the Royal Society B:Biological Sciences, 1984, 221(1222): 87–102. doi: 10.1098/rspb.1984.0024. [10] IZHIKEVICH E M. Simple model of spiking neurons[J]. IEEE Transactions on Neural Networks, 2003, 14(6): 1569–1572. doi: 10.1109/TNN.2003.820440. [11] 马军. 功能神经元建模及动力学若干问题[J]. 广西师范大学学报:自然科学版, 2022, 40(5): 307–323. doi: 10.16088/j.issn.1001-6600.2021122301.MA Jun. Dynamics and model approach for functional neurons[J]. Journal of Guangxi Normal University:Natural Science Edition, 2022, 40(5): 307–323. doi: 10.16088/j.issn.1001-6600.2021122301. [12] LIU Yong, XU Wanjiang, MA Jun, et al. A new photosensitive neuron model and its dynamics[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1387–1396. doi: 10.1631/FITEE.1900606. [13] YAO Zhao, SUN Kehui, and HE Shaobo. Firing patterns in a fractional-order FithzHugh–Nagumo neuron model[J]. Nonlinear Dynamics, 2022, 110(2): 1807–1822. doi: 10.1007/s11071-022-07690-2. [14] YANG Xin and ZHANG Guangjun. The synchronization behaviors of memristive synapse-coupled fractional-order neuronal networks[J]. IEEE Access, 2021, 9: 131844–131857. doi: 10.1109/ACCESS.2021.3115149. [15] ABDELATY A M, FOUDA M E, and ELTAWIL A M. On numerical approximations of fractional-order spiking neuron models[J]. Communications in Nonlinear Science and Numerical Simulation, 2022, 105: 106078. doi: 10.1016/j.cnsns.2021.106078. [16] 谢盈, 朱志刚, 张晓锋, 等. 光电流驱动下非线性神经元电路的放电模式控制[J]. 物理学报, 2021, 70(21): 210502. doi: 10.7498/aps.70.20210676.XIE Ying, ZHU Zhigang, ZHANG Xiaofeng, et al. Control of firing mode in nonlinear neuron circuit driven by photocurrent[J]. Acta Physica Sinica, 2021, 70(21): 210502. doi: 10.7498/aps.70.20210676. [17] WESTERLUND S and EKSTAM L. Capacitor theory[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 1994, 1(5): 826–839. doi: 10.1109/94.326654. [18] OLDHAM K B and SPANIER J. The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order[M]. Amsterdam: Elsevier, 1974. [19] GAO Guanghua, SUN Zhizhong, and ZHANG Hongwei. A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications[J]. Journal of Computational Physics, 2014, 259: 33–50. doi: 10.1016/j.jcp.2013.11.017. -
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