Rotation-controlled Wilson-Cowan neuron model and its hardware

Abstract

Various biological neuron models have been defined by using nonlinear function definitions in order to explain the characteristic dynamics of neurons that are the basic elements of the communication network in the living body. In the analysis of these models, the solution methods used in the analysis of nonlinear systems are frequently used. In recent years, some of the studies about nonlinear systems have been encountered with the rotational attractor structures. In this study, it is aimed to provide phase control of the rotational attractor obtained by applying the Euler Rotation Theorem to the Wilson Cowan (W-C) neuron model that is used effectively in the literature to define excitatory and inhibitory synapse structures. In addition, the FPGA (Field Programmable Gate Array)-based hardware implementation study of the rotation-controlled W-C neuron model have also been carried out in order to see its usability in studies required to the real-time signals. With the numerical analyzes, it has been seen that the attractor structure of the rotation-controlled W-C neuron model can be controlled successfully. On the other hand, an alternative study has been reported for the systems designed by inspiring the biology and emulated with electronic equipment.

Keywords

• Wilson-Cowan neuron model
• Excitatory and inhibitory synapse
• Euler rotation theorem
• Nonlinear systems
• Field programmable gate array (FPGA)

Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi

Öz

Canlı vücudundaki iletişim ağının temel elemanı olan nöronların karakteristik dinamiklerini açıklamak için, doğrusal olmayan fonksiyon tanımlamalarından yararlanılarak çeşitli biyolojik nöron modelleri tanımlanmıştır. Bu modellerin analizlerinde, doğrusal olmayan sistemlerin analizlerinde kullanılan çözüm yöntemlerinden sıklıkla yararlanılmaktadır. Son yıllarda doğrusal olmayan sistemleri konu alan çalışmaların bir kısmında rotasyonlu çeker yapıları ile karşılaşılmaktadır. Bu çalışmada, literatürde uyarıcı ve engelleyici sinaps yapılarını tanımlamada etkin kullanılan Wilson Cowan (W-C) nöron modeline Euler Rotasyon Teoremi’nin uygulanması ile elde edilen rotasyonlu çekerin faz kontrolünün sağlanması amaçlanmıştır. Ayrıca, gerçek zamanlı işaretlere ihtiyaç duyulabilecek çalışmalarda kullanılabilirliğinin gösterilmesi amacı ile rotasyon kontrollü W-C nöron modelinin FPGA (Field Programmable Gate Array) tabanlı donanım gerçekleştirim çalışması da yapılmıştır. Yapılan nümerik analizler ile rotasyon kontrollü W-C nöron modelinin çeker yapısının başarılı bir şekilde kontrol edilebildiği görülmüştür. Öte yandan deneysel gerçekleştirim çalışmaları ile biyolojiden esinlenilerek tasarlanan ve elektronik ekipmanlarla taklit edilen sistemler için alternatif bir çalışma kaydedilmiştir.

Anahtar Kelimeler

• Wilson-Cowan Nöron Modeli
• Uyarıcı ve Engelleyici Sinaps
• Euler Rotasyon Teoremi
• Doğrusal Olmayan Sistemler
• Alan Programlanabilir Kapı Dizisi (FPGA)

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