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

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

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.

Keywords:

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

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