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

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.

Keywords

• Izhikevich Neuron Model
• Chemically Coupling
• Synchronization
• Lyapunov Control Method.

Kimyasal Kuplajlı Izhikevich Nöron Modelinin Lyapunov Kontrol Metodu ile Senkronizasyonu

Öz

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.

Anahtar Kelimeler

• Izhikevich Nöron Modeli
• Kimyasal Kuplaj
• Senkronizasyon
• Lyapunov Kontrol Metodu

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