A review of neuron map models and their roles in neural systems and neuromorphological engineering

Öz

Neurons are the fundamental building blocks of communication between the central nervous system and sensory organs in the living beings. Neuron cell membrane potentials, cell recovery states, voltage gate ions, and the rich complex dynamics generated by the cell membrane are represented by biological neuron models defined by the ordinary differential equations. Various discretization methods are utilized in the numerical solutions of these systems. However, in recent years, instead of these continuous time based models, the neuron map models, which are defined in discrete time and do not require discretization process, are also introduced to the literature. This study re-observes the neuronal dynamics exhibited by the recently popularized Rulkov, Chialvo, Courbage–Nekorkin–Vdovin, and Huber-Braun neuron map models through their numerical simulations. It is aimed to present a review of the usage of these models in common research areas on biological neuron models, so to present a review study that is thought to be a source of inspiration for open research study topics for the researchers working on neuromorphological engineering topics.

Anahtar Kelimeler

• Rulkov neuron map model
• Chialvo neuron map model
• Courbage–Nekorkin–Vdovin neuron map model
• Huber-Braun neuron map model
• synchronization
• noise
• hardware

Nöron harita modelleri ve bu modellerin nöral sistemler ve nöromorfolojik mühendislik alanlarındaki rolleri üzerine bir derleme

Öz

Canlı vücudunda merkezi sinir sistemi ile duyu organları arasındaki iletişimin temel yapı taşı nöronlardır. Nöronların hücre zarı potansiyelleri, hücrelerin toparlanma durumları, voltaj kapı iyonları ve hücre zarının ürettiği zengin kompleks dinamikler adi diferansiyel denklem tanımlamalarına sahip biyolojik nöron modelleri ile temsil edilmektedir. Bu sistemlerin nümerik çözümlerinde çeşitli ayrıklaştırma yöntemlerinden yararlanılmaktadır. Bununla birlikte, son yıllarda sürekli zamanda tanımlanan bu modeller yerine, ayrıklaştırma sürecine ihtiyaç duymayan ve ayrık zamanda tanımlanan nöron harita modelleri literatüre sunulmaktadır. Bu çalışmada son zamanlarda kullanımı yaygınlaşan Rulkov, Chialvo, Courbage–Nekorkin–Vdovin ve Huber-Braun nöron harita modellerinin sergiledikleri nöronal dinamikler nümerik simülasyonlarla yeniden gözlemlenmektedir. Bu modellerin biyolojik nöron modelleri üzerine yapılan yaygın araştırma alanlarındaki kullanımları ile ilgili bir derleme sunmak amaçlanmakta ve böylece nöromorfolojik mühendislik konuları üzerine çalışan araştırmacılara, araştırmaya açık çalışma konuları için ilham kaynağı olabileceği düşünülen bir derleme çalışmasının ortaya konması hedeflenmektedir.

Anahtar Kelimeler

• Rulkov nöron harita modeli
• Chialvo nöron harita modeli
• Courbage–Nekorkin–Vdovin nöron harita modeli
• Huber-Braun nöron harita modeli
• senkronizasyon
• gürültü
• donanım.

Kaynakça

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