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Journals / Avrupa Bilim ve Teknoloji Dergisi / 2026 / Sayı: 32 Özel Sayı

Synchronization of the Chemically Coupled Izhikevich Neuron Model with the Lyapunov Control Method

Kimyasal Kuplajlı Izhikevich Nöron Modelinin Lyapunov Kontrol Metodu ile Senkronizasyonu

Zühra Karaca(NİĞDE ÖMER HALİSDEMİR ÜNİVERSİTESİ)0000-0002-3921-604X
Nimet Korkmaz(Kayseri University)0000-0002-7419-1538
Yasemin Altuncu(NİĞDE ÖMER HALİSDEMİR ÜNİVERSİTESİ)0000-0003-1517-8090
Recai Kılıç(ERCİYES ÜNİVERSİTESİ)0000-0002-5069-6603
Pages
736–740
Publication Date
2021-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, it has been shown that the system with the Lyapunov control method is fired synchronously regardless of the changes in the value of the synaptic coupling weight.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Although there are many studies on the electrically coupled Izhikevich neuron model in the literature, the study of the chemically coupled structure is limited.
📊
Key Findings & Data:The synchronization of bidirectional chemically coupled Izhikevich neurons with the Lyapunov control method is discussed for the first time in this study.
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Conclusion & Impact:Finally, it has been shown that the system with the Lyapunov control method is fired synchronously regardless of the changes in the value of the synaptic coupling weight.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Izhikevich Nöron Modeli · Kimyasal Kuplaj · Senkronizasyon

Abstract

Although there are many studies on the electrically coupled Izhikevich neuron model in the literature, the study of the chemically coupled structure is limited. The synchronization of bidirectional chemically coupled Izhikevich neurons with the Lyapunov control method is discussed for the first time in this study. Standard deviation results are given to observe the effect of the coupling weight of the coupled neurons. With the Lyapunov controller applied to one of the coupled neurons, the control of whether the neurons are synchronized regardless of the coupling weight was also observed by means of standard deviation analysis. Finally, it has been shown that the system with the Lyapunov control method is fired synchronously regardless of the changes in the value of the synaptic coupling weight.

Özet

Literatürde, elektriksel kuplajlı Izhikevich nöron modeline ait birçok çalışma olmasına rağmen kimyasal kuplajlı yapıya ait inceleme sınırlı sayıdadır. Çift yönlü kimyasal olarak kuplajlanan iki adet Izhikevich nöronunun Lyapunov kontrol yöntemiyle senkronizasyonu ilk defa bu çalışmada ele alınmıştır. Kuplajlanan nöronların kuplajlama ağırlığının etkisini gözlemlemek için standart sapma sonuçları verilmiştir. Kuplajlanan nöronlardan birine uygulanan Lyapunov kontrolörü ile, nöronların kuplajlama ağırlığından bağımsız şekilde senkron hale gelip gelmediğinin kontrolü yine standart sapma analizi vasıtası ile gözlemlenmiştir. Son olarak, Lyapunov kontrol yöntemi uygulanan sistemin, sinaptik kuplajlama ağırlık değerinin değişikliklerinden bağımsız bir şekilde senkron olarak ateşlendiği gösterilmiştir.

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Cite This Article

Karaca, Z., Korkmaz, N., Altuncu, Y., Kılıç, R. (2021). Synchronization of the Chemically Coupled Izhikevich Neuron Model with the Lyapunov Control Method. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 32 Özel Sayı, 736–740. https://doi.org/10.31590/ejosat.1042337

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References (25)

  1. Bin, D., Jiang, W., & Xiangyang, F. (2006). Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solitons & Fractals, 29(1), 182–189. https://doi.org/10.1016/j.chaos.2005.08.027
  2. Bizzarri, F., Brambilla, A., Gajani, G. S. (2013). Lyapunov exponents computation for hybrid neurons. J. Comput. Neurosci., 35(2), 201-212. doi: 10.1007/s10827-013-0448-6.
  3. Cakir, Y. (2017). Modeling of time delay-induced multiple synchronization behavior of interneuronal networks with the Izhikevich neuron model. Turk. J. Electr. Eng. Comput. Sci., 25, 2595–2605.
  4. Che, Y., Zhang, S., Wang, J., Cui, S., Han, C., Deng, B., & Wei, X. (2011). Synchronization of inhibitory coupled Hindmarsh-Rose neurons via adaptive sliding mode control. 2011 2nd International Conference on Intelligent Control and Information Processing, 2, 1134–1139. https://doi.org/10.1109/ICICIP.2011.6008431
  5. Dhamala, M., Jirsa, V. K. & Ding, M.(2004). Enhancement of neural synchrony by time delay. Phys. Rev. Lett. 92, 074104.
  6. FitzHugh, R., Mathematical models for excitation and propagation in nerve, Schawn,H.P. (ed.) biological Engineering, McGraw-Hill, New York, 1969.
  7. Hindmarsh, J. L., Rose, R. M., & Huxley, A. F. (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(1222), 87–102. https://doi.org/10.1098/rspb.1984.0024
  8. 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(4), 500–544.
  9. Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569–1572. https://doi.org/10.1109/TNN.2003.820440
  10. Khoshkhou, M., & Montakhab, A. (2018). Beta-Rhythm Oscillations and Synchronization Transition in Network Models of Izhikevich Neurons: Effect of Topology and Synaptic Type. Frontiers in Computational Neuroscience, 12. https://doi.org/10.3389/fncom.2018.00059
  11. Kim, Y. (2010).Identification of dynamical states in stimulated Izhikevich neuron models by using a 0-1 test. Journal of the Korean Physical Society, 57(6), 1363-1368. Doi: 10.3938/jkps.57.1363.
  12. Kuang, S., & Cong, S. (2008). Lyapunov control methods of closed quantum systems.Automatica,44(1),98–108. https://doi.org/10.1016/j.automatica.2007.05.013
  13. La Rosa, M., Rabinovich, M. I., Huerta, R., Abarbanel, H. D. I. & Fortuna, L.(2000). Slow regularization through chaotic oscillation transfer in an unidirectional chain of Hindmarsh–Rose models. Phys. Lett. A 266(1), 88-93.
  14. Lynch, S. (2004). Dynamical systems with applications using MATLAB. Boston: Birkhäuser.
  15. Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35(1), 193–213. https://doi.org/10.1016/S0006-3495(81)84782-0
  16. Nguyen, L. H., & Hong, K.-S. (2011). Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions. Mathematics and Computers in Simulation, 82(4), 590–603. https://doi.org/10.1016/j.matcom.2011.10.005
  17. Nobukawa, S., & Nishimura, H. (2015). Stochastic resonance effects in Izhikevich neural system with spike-timing dependent plasticity. 2015 54th AnnualConference of the Society of Instrument and Control Engineers of Japan (SICE), 270–275. https://doi.org/10.1109/SICE.2015.7285324
  18. Nobukawa, S., Nishimura, H., & Yamanishi, T. (2017). Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model. Scientific Reports, 7(1), 1331. https://doi.org/10.1038/s41598-017-01511-y
  19. Sabbagh, H. (2000). Control of chaotic solutions of the Hindmarsh–Rose equations. Chaos Soliton. Fract. 11(8), 1213-1218.
  20. Shi, Y., Wang, J., Deng, B., & Liu, Q. (2009). Chaotic Synchronization of Coupled Hindmarsh-Rose Neurons Using Adaptive Control. 2009 2nd International Conference on Biomedical Engineering and Informatics, 1–5. https://doi.org/10.1109/BMEI.2009.5302804
  21. Wang, W., Perez, G. &Cerdeira, H. A. (1993). Dynamical behavior of the firings in a coupled neuronal system. Phys. Rev. E. 47(4), 2893-2898.
  22. Wang, Q. Y., Lu, Q. S., Chen, G. R., & Guo, D. H. (2006). Chaos synchronization of coupled neurons with gap junctions. Physics Letters A, 356(1), 17–25. https://doi.org/10.1016/j.physleta.2006.03.017
  23. Wilson, H. R., & Cowan, J. D. (1972). Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophysical Journal, 12(1), 1–24.
  24. Yu, H. and Peng, J. (2006). Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems. Chaos Soliton. Fract., 29(2), 342-348.
  25. Zhang, T., Wang, J., Fei, X., & Deng, B. (2007). Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control. Chaos, Solitons & Fractals, 33(1), 194–202. https://doi.org/10.1016/j.chaos.2006.01.037