Elektromanyetik Alan Etkili Fitzhugh-Nagumo Nöron Modeline Rotasyon Kontrol İşleminin Uygulanması

Öz

Biyolojik nöron modellerinin kararlılık analizlerinin yapılması ve dinamik davranışlarının kontrolü üzerine literatürde pek çok çalışma mevcuttur. Son zamanlarda biyolojik sistemler, lazer sistemleri, kaotik sistemler ve nöral sistemler gibi doğrusal olmayan tanımlamalara sahip yapılarda, rotasyonel dinamikler gözlemlenmektedir. Bu rotasyonel dinamiklerin modellenmesi üzerine çalışmalar yapılmaktadır. Burada da elektromanyetik alan etkili Fitzhugh-Nagumo nöron modelinin hücre zarı potansiyeli ve transmembrane akımlarının oluşturduğu çekerlerin rotasyon kontrolünün Euler Rotasyon Teoremi kullanılarak yapılması amaçlanmaktadır. Elektromanyetik alan etkili Fitzhugh-Nagumo nöron modeli elektromanyetik alan tanımlamasının ilave bir durum değişkeni olarak tanımlanması ile geliştirilen bir tanımlamaya sahip olması yönüyle diğer modellerden farklılaşmaktadır. Bu modeldeki harici uyaran bir sinüzoidal kaynak şeklinde seçilerek, kaynağın genliğinin nöron modeli dinamiklerine etkisi; dallanma diyagramından, zaman domeni gösterimlerinden ve Lyapunov üstellerinden yararlanılarak gözlemlenecektir. Rotasyon kontrol işleminin başarım sonuçları, modeldeki harici akım kaynağının farklı genlik değerleri için kaydedilen nümerik simülasyon sonuçları ile paylaşılacaktır.

Anahtar Kelimeler

• Elektromanyetik Alan
• Biyolojik Nöron Modeli
• Fitzhugh-Nagumo
• Rotasyon Kontrol
• Dallanma Diyagramı
• Lyapunov Üsteli

The Application of the Rotation Control Process to the Electromagnetic Field-Effect Fitzhugh-Nagumo Neuron Model

Öz

There are many studies about the stability analysis of the biological neuron models and the control of their dynamic behavior in the literature. Recently, the rotational dynamics have been observed in structures, which have nonlinear definitions, such as biological systems, laser systems, chaotic systems and neural systems. Several studies are carried out about the modeling of these rotational dynamics. Here, it is aimed to control the rotation of the attractors, which are formed by the membrane potential and the transmembrane currents of the electromagnetic field-effect Fitzhugh-Nagumo neuron model and it is used the Euler Rotation Theorem. The electromagnetic field-effect Fitzhugh-Nagumo neuron model differs from other models with its following aspect. This model has an additional state variable that describes the electromagnetic field effect. The effects of the amplitude of the external stimulus on the dynamics of this neuron model are observed by utilizing the bifurcation diagram, time domain representations and Lyapunov exponents and this external stimulus is selected as a sinusoidal source. The performance results of the rotation control process are shared with the numerical simulation results that are recorded for the different amplitude values of the external current source in this model.

Anahtar Kelimeler

• Electromagnetic Field
• Biological Neuron Model
• Fitzhugh-Nagumo
• Rotation Control
• Bifurcation Diagram
• Lyapunov Exponent

Kaynakça

1. [1] Chua, L. 1971. Memristor-the missing circuit element. IEEE Transactions on Circuit Theory, 18 (5), 507-519.
2. [2] 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(3), 1479-1490.
3. [3] Lv, M., Ma, J. 2016. Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing, 205, 375-381.
4. [4] Xu, Q., Song, Z., Bao, H., Chen, M., Bao, B. 2018. Two-neuron-based non-autonomous memristive Hopfield neural network: Numerical analyses and hardware experiments. AEU-International Journal of Electronics and Communications, 96, 66-74.
5. [5] Hodgkin, A.L., Andrew F.H. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology, 117(4), 500.
6. [6] FitzHugh, R. 1961. Impulses and physiological states in theoretical models of nerve membrane. Biophysical journal, 1(6), 445-466.
7. [7] 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(1222), 87-102.
8. [8] Wu, F., Wang, C., Xu, Y., Ma, J. 2016. Model of electrical activity in cardiac tissue under electromagnetic induction. Scientific reports, 6(1), 1-12.

9. [9] Ma, J., Wu, F., Hayat, T., Zhou, P., Tang, J. 2017. Electromagnetic induction and radiation-induced abnormality of wave propagation in excitable media. Physica A: Statistical Mechanics and its Applications, 486, 508-516.
10. [10] Bao, B., Hu, A., Bao, H., Xu, Q., Chen, M., Wu, H. 2018. Three-dimensional memristive Hindmarsh–Rose neuron model with hidden coexisting asymmetric behaviors. Complexity, 2018.
11. [11] Bao, H., Hu, A., Liu, W., Bao, B. 2019. Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Transactions on Neural Networks and Learning Systems, 31(2), 502-511.
12. [12] Lin, H., Wang, C., Sun, Y., Yao, W. 2020. Firing multistability in a locally active memristive neuron model. Nonlinear Dynamics, 100(4), 3667-3683.
13. [13] Bao, B., Zhu, Y., Ma, J., Bao, H., Wu, H., Chen, M. 2021. Memristive neuron model with an adapting synapse and its hardware experiments. Science China Technological Sciences, 64(5), 1107-1117.
14. [14] Ma, J., Zhang, G., Hayat, T., Ren, G. 2019. Model electrical activity of neuron under electric field. Nonlinear dynamics, 95(2), 1585-1598.
15. [15] 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.
16. [16] Bizzarri, F., Brambilla, A., Storti Gajani, G. 2013. Lyapunov exponents computation for hybrid neurons. Journal of computational neuroscience, 35(2), 201-212.
17. [17] Çimen, Z., Korkmaz, N., Altuncu, Y., Kılıç, R. 2020. Evaluating the effectiveness of several synchronization control methods applying to the electrically and the chemically coupled hindmarsh-rose neurons. Biosystems, 198, 104284.
18. [18] Thottil, S. K., Ignatius, R. P. 2017. Nonlinear feedback coupling in Hindmarsh–Rose neurons. Nonlinear Dynamics, 87(3), 1879-1899.
19. [19] Karaca, Z., Korkmaz, N., Altuncu, Y., Kılıç, R. 2021. An extensive FPGA-based realization study about the Izhikevich neurons and their bio-inspired applications. Nonlinear Dynamics, 105(4), 3529-3549.
20. [20] Kim, M. Y., Roy, R., Aron, J. L., Carr, T. W., Schwartz, I. B. 2005. Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment. Physical review letters, 94(8), 088101.
21. [21] Prasad, A., Dana, S. K., Karnatak, R., Kurths, J., Blasius, B., & Ramaswamy, R. 2008. Universal occurrence of the phase-flip bifurcation in time-delay coupled systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 18(2), 023111.
22. [22] Korkmaz, N. 2021. A Phase Control Method for the Dynamical Attractor of the HR Neuron Model: The Rotation-Transition Process and Its Experimental Realization. Neural Processing Letters, 53(6), 3877-3892.
23. [23] Arfken G.B., Weber H.J. 1999. Mathematical methods for physicists, 6th edn. Elsevier Academic Press, Cambridge, 1205s. ISBN 0-12-088584-0