The Kuramoto model has been the focus of extensive research and provides a system that can model synchronisation and desynchronisation in groups of coupled oscillators. The limited variety of states that the Kuramoto model can attain makes it suitable for modelling certain aspects of some neuroscientific systems but does not allow enough rich dynamics to model more complex systems. However, various modifications to the standard Kuramoto model have been made in order to enable it to be used as a model for alternative, specific applications.
Traditional neuron models, such as the Hodgkin-Huxley model, consider precise measurements of the membrane potential of cells in the system and evaluate these values at the point of neuronal spiking and along the action potential. On the other hand, models based around the Kuramoto model consider only the timing and frequency of when the neurons are firing in relation to the other neurons in the system. While analysing and adapting these systems to model realistic neuroscientific patterns it is not important to consider an absolute time-scale of when each neuron fires and instead it is only important to consider relational time series of when neurons are `firing' (ie. their phase) in relation to the other parts of the system.
The main goal of the Kuramoto model is to explain synchronisation from unsynchronised oscillator sources. It can be seen that a collection of metronomes on a plank of wood that is not fixed in place will eventually synchronise (watch the video here by Bryan Daniels), even when the metronomes are started out of phase and with different forcing strength. The Kuramoto model therefore explains how these systems either enter a synchronous and anti-synchronous state. Since it's creation, the Kuramoto model has been adapted to a vast range of physical problems and research, for instance, with Landau damping in plasmas [9].
The main goal of the Kuramoto model is to explain synchronisation from unsynchronised oscillator sources. It can be seen that a collection of metronomes on a plank of wood that is not fixed in place will eventually synchronise (watch the video here by Bryan Daniels), even when the metronomes are started out of phase and with different forcing strength. The Kuramoto model therefore explains how these systems either enter a synchronous and anti-synchronous state. Since it's creation, the Kuramoto model has been adapted to a vast range of physical problems and research, for instance, with Landau damping in plasmas [9].
