Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu

Öz

Bu çalışmada, elektriksel ve kimyasal kuplajlı iki Izhikevich nöron modelinin geri adımlamalı kontrol yöntemi kullanılarak senkronizasyonu ele alınmıştır. Literatürde elektriksel olarak kuplajlanan Izhikevich nöron modeliyle yapılan çalışma sayısı fazlayken, kimyasal kuplaj ile oluşturulan yapıya ait çalışmalar sınırlıdır ve çift yönlü kimyasal olarak kuplajlanan Izhikevich nöron modelinin geri adımlamalı kontrol yöntemi kullanılarak senkronizasyonu ilk defa bu çalışmada ele alınmıştır. Geri adımlamalı kontrol yönteminin uygulandığı sistemin, kuplajlama ağırlığından bağımsız bir şekilde eş zamanlı olarak ateşlendiği, hem standart sapma analizi ile hem de simülasyon sonuçları gösterilmiştir.

Anahtar Kelimeler

• Izhikevich nöron modeli
• Senkronizasyon
• Geri adımlamalı kontrol yöntemi
• Kimyasal kuplaj.

Synchronization of electrically and chemically coupled ızhikevich neuron model via backstepping control method

Öz

This study addresses the synchronization of two Izhikevich neuron models, coupled electrically and chemically, using the backstepping control method. While there are numerous studies in the literature regarding the electrical coupling of Izhikevich neuron models, research on synchronization of structures created through chemical coupling is limited. This study is the first to tackle the synchronization of a bidirectionally chemically coupled Izhikevich neuron model using the backstepping control method. The system subjected to the backstepping control method was observed to trigger synchronization independently of the coupling weight. This observation is confirmed through both standard deviation analysis and simulation results.

Anahtar Kelimeler

• Izhikevich neuron model
• Synchronization
• Backstepping control method
• Chemically coupling.

Kaynakça

1. A.E. Pereda, Electrical synapses and their functional interactions with chemical synapses, Nat Rev Neurosci., 15(4), 250-263, 2014. https://doi.org/10.10 38/nrn3708.
2. A. L. Hodgkin and A. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology 117 (4), 500-544, 1952. https://doi.org/10 .1016/S0092-8240(05)80004-7.
3. H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal 12 (1), 1–24, 1972. https://doi.org/10.1016/S0006-3495(72)86068-5.
4. R. FitzHugh, Mathematical models for excitation and propagation in nerve, Schawn,H.P., McGraw-Hill, New York, 1969.
5. C. Morris and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal 35 (1), 193–213, 1981. https://doi.org/10.1016/S0006-3495(81)84782-0.
6. J. Hindmarsh and R. M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proceedings of the Royal Society of London. Series B. Biological Sciences 221 (1222), 87-102,1984. https://doi.org/10.1098/rspb.1984.0024.
7. E. M. Izhikevich, Simple model of spiking neurons, IEEE Trans. Neural Networks 14(6), 1569–1572, Nov. 2003. https://doi.org/10.1109/TNN.2003.820440.
8. S. A. Malik, A. H. Mir, Synchronization of Hindmarsh Rose Neurons, Neural Networks, 123, 372-380, 2020. https://doi.org/10.1016/j.neunet.2019.11.024.

9. H. Yu, J. Peng, Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems. Chaos, Solit. Fractals 29 (2), 342–348 2006. https://doi .org/10.1016/j.chaos.2005.08.075.
10. Z. Çimen, N. Korkmaz, Y. Altuncu, R. Kılıç, Evaluating the effectiveness of several synchronization control methods applying to the electrically and the chemically coupled hindmarsh-rose neurons, Biosystems, 198, 1-14, 2020. https://doi.org/10.1016/j. biosystems.2020.104284.
11. Z.Karaca, N. Korkmaz, Y. Altuncu, R.Kılıç, An extensive FPGA-based realization study about the Izhikevich neurons and their bio-inspired applications. Nonlinear Dyn 105, 3529–3549, 2021. https://doi.org /10.1007/s11071-021-06647-1.
12. C.-H. Li, S.-Y. Yang, Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of Hindmarsh–Rose neurons,Applied Mathematical Modelling, Vol. 39(21), 6631-6644, 2015. https://doi.org/10.1016/j.apm.2015.02.017.
13. Y. Che, J. Wang, K. M. Tsang, W. L. Chan, Unidirectional synchronization for Hindmarsh-Rose neurons via robust adaptive sliding mode control. Nonlinear Analysis: Real World Applications, 11(2), 1096-1104, 2010. https://doi.org/10.1016/j.nonrwa. 2009.02.004.
14. X. Liu, & C. Tianping, Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix, Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387 (16), 4429-4439, 2008. https://doi.org/10.1016/j.physa.2008 .03.005.
15. D. Bin, W. Jiang and F. Xiangyang, Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control, Chaos, Solitons & Fractals, 29 (1), 182–89, 2006. http://doi. org/10.1016/j.chaos.2005.08.027.
16. S. Zhang, E. -M. Yong, Y. Zhou and W. -Q. Qian, Dynamic backstepping control for pure-feedback non-linear systems, in IMA Journal of Mathematical Control and Information, 37 (1), 670-693, 2020, http:// doi.org/10.1093/imamci/dnz019.
17. H. K. Khalil, and J. W. Grizzle, Nonlinear Systems, Prentice Hall, Upper Saddle River, New Jersey, 2002.
18. S. H. Yu, , C. H. Hyunand and M. N. Park, Backstepping control and synchronization for 4-D Lorenz-Stenflo chaotic system with single input, International Journal of Fuzzy Logic and Intelligent Systems 11(3), 143-148, 2011. https://doi.org/10.5391 /ijfis.2011.11.3.143.
19. S. Vaidyanathan, A. T. Azar, Backstepping Control of Nonlinear Dynamical Systems 1st, Academic Press, Elsevier, 2020
20. Z. Karaca, N. Korkmaz, Y. Altuncu &R. Kılıç, Kimyasal Kuplajlı Izhikevich Nöron Modelinin Lyapunov Kontrol Metodu ile Senkronizasyonu. Avrupa Bilim ve Teknoloji Dergisi, Ejosat Özel Sayı (RDCONF), 736-740, 2021. http://doi.org/10.31590/ ejosat.1042337
21. N. Korkmaz, İ. Öztürk, A. Kalınlı, and R. Kılıç, Hardware verification: Determining the parameters of the modified Izhikevich neuron model with genetic algorithm, 10th International Conference on Electrical and Electronics Engineering (ELECO), pp. 588-592, Bursa, 30, 2017.
22. E. M. Izhikevich, Which model to use for cortical spiking neurons?, IEEE Transactions on Neural Networks 15(5), 1063-1070, 2004. https://doi.org/10 .1109/TNN.2004.832719.
23. S. Lynch, Dynamical systems with applications using MATLAB. Boston: Birkhäuser. 2004.
24. B. Deng, J. Wang, X. Fei, Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solit. Fractals 29, 182–189. 2006. https://doi.org/10.1016/j.chaos.2005.08.027
25. C. C. Peng, & C. L. Chen,Robust chaotic control of Lorenz system by backstepping design. Chaos, Solitons Fractals, 37(2), 598–608, 2008 https://doi.org/10.101 6/J.CHAOS.2006.09.057.
26. Z. Karaca, N. Korkmaz, Y. Altuncu and R. Kılıç, An extensive FPGA-based realization study about the Izhikevich neurons and their bio-inspired applications. Nonlinear Dyn 105, 3529–3549, 2021. https://doi.org/ 10.1007/s11071-021-06647-1.