Exploring neuronal dynamics through the Izhikevich and Kuramoto models

Abstract

There are different mathematical models to describe the behavior of neurons, and with different levels of accuracy. In this study, we explored two major models, the biologically realistic Izhikevich model and the less realistic but convenient Kuramoto oscillator. We compared them to investigate whether it is correct to use Kuramoto oscillators to describe collective dynamics, such as synchronization, in large populations of realistic Izhikevich neuronal networks. We show that this is indeed the case when the number of Izhikevich neurons is large, which is demonstrated by coupling 5 groups of Izhikevich 1000 neurons each and showing that the whole system can be simplified as the sum of 5 coupled Kuramoto oscillators