Generalising the Kuramoto model for the study of neuronal synchronisation in the brain

In this article, we have generalised the Kuramoto model to allow one to model neuronal synchronisation more appropriately. The generalised version allows for different connective arrangements, time-varying natural frequencies and time-varying coupling strengths to be realised within the framework of the original Kuramoto model. By incorporating the above mentioned features into the original Kuramoto model one can allow for the adaptive nature of neurons in the brain to be accommodated. Extensive tests using the generalised Kuramoto model were performed on a N = 4 coupled oscillator network. Examination of how different connective arrangements, time-varying natural frequencies and time-varying coupling strengths affected synchronisation separately and in combination are reported. The effects on synchronisation for large N are also reported.