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

Yıl 2023, Cilt: 12 Sayı: 4, 1581 - 1587, 15.10.2023
https://doi.org/10.28948/ngumuh.1340148

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.

Kaynakça

  • 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.
  • 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.
  • 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.
  • R. FitzHugh, Mathematical models for excitation and propagation in nerve, Schawn,H.P., McGraw-Hill, New York, 1969.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • H. K. Khalil, and J. W. Grizzle, Nonlinear Systems, Prentice Hall, Upper Saddle River, New Jersey, 2002.
  • 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.
  • S. Vaidyanathan, A. T. Azar, Backstepping Control of Nonlinear Dynamical Systems 1st, Academic Press, Elsevier, 2020
  • 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
  • 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.
  • 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.
  • S. Lynch, Dynamical systems with applications using MATLAB. Boston: Birkhäuser. 2004.
  • 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
  • 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.
  • 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.

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

Yıl 2023, Cilt: 12 Sayı: 4, 1581 - 1587, 15.10.2023
https://doi.org/10.28948/ngumuh.1340148

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.

Kaynakça

  • 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.
  • 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.
  • 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.
  • R. FitzHugh, Mathematical models for excitation and propagation in nerve, Schawn,H.P., McGraw-Hill, New York, 1969.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • H. K. Khalil, and J. W. Grizzle, Nonlinear Systems, Prentice Hall, Upper Saddle River, New Jersey, 2002.
  • 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.
  • S. Vaidyanathan, A. T. Azar, Backstepping Control of Nonlinear Dynamical Systems 1st, Academic Press, Elsevier, 2020
  • 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
  • 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.
  • 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.
  • S. Lynch, Dynamical systems with applications using MATLAB. Boston: Birkhäuser. 2004.
  • 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
  • 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.
  • 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.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Elektronik
Bölüm Makaleler
Yazarlar

Zühra Karaca 0000-0002-3921-604X

Nimet Korkmaz 0000-0002-7419-1538

Recai Kılıç 0000-0002-5069-6603

Erken Görünüm Tarihi 25 Eylül 2023
Yayımlanma Tarihi 15 Ekim 2023
Gönderilme Tarihi 9 Ağustos 2023
Kabul Tarihi 20 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 12 Sayı: 4

Kaynak Göster

APA Karaca, Z., Korkmaz, N., & Kılıç, R. (2023). Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 12(4), 1581-1587. https://doi.org/10.28948/ngumuh.1340148
AMA Karaca Z, Korkmaz N, Kılıç R. Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu. NÖHÜ Müh. Bilim. Derg. Ekim 2023;12(4):1581-1587. doi:10.28948/ngumuh.1340148
Chicago Karaca, Zühra, Nimet Korkmaz, ve Recai Kılıç. “Elektriksel Ve Kimyasal Kuplajlı ızhikevich nöron Modelinin Geri adımlamalı Kontrol yöntemi Ile Senkronizasyonu”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 12, sy. 4 (Ekim 2023): 1581-87. https://doi.org/10.28948/ngumuh.1340148.
EndNote Karaca Z, Korkmaz N, Kılıç R (01 Ekim 2023) Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 12 4 1581–1587.
IEEE Z. Karaca, N. Korkmaz, ve R. Kılıç, “Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu”, NÖHÜ Müh. Bilim. Derg., c. 12, sy. 4, ss. 1581–1587, 2023, doi: 10.28948/ngumuh.1340148.
ISNAD Karaca, Zühra vd. “Elektriksel Ve Kimyasal Kuplajlı ızhikevich nöron Modelinin Geri adımlamalı Kontrol yöntemi Ile Senkronizasyonu”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 12/4 (Ekim 2023), 1581-1587. https://doi.org/10.28948/ngumuh.1340148.
JAMA Karaca Z, Korkmaz N, Kılıç R. Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu. NÖHÜ Müh. Bilim. Derg. 2023;12:1581–1587.
MLA Karaca, Zühra vd. “Elektriksel Ve Kimyasal Kuplajlı ızhikevich nöron Modelinin Geri adımlamalı Kontrol yöntemi Ile Senkronizasyonu”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, c. 12, sy. 4, 2023, ss. 1581-7, doi:10.28948/ngumuh.1340148.
Vancouver Karaca Z, Korkmaz N, Kılıç R. Elektriksel ve kimyasal kuplajlı ızhikevich nöron modelinin geri adımlamalı kontrol yöntemi ile senkronizasyonu. NÖHÜ Müh. Bilim. Derg. 2023;12(4):1581-7.

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