To finish off with we take a quick look at some of the variations that have been made to the Kuramoto model that have widened it's application in real-world system modelling. The Kuramoto model has been used in a vast number of models, some of which have direct application, such as with deep-brain stimulation of patients with Parkinson's disease.
First we consider the effect of noise on the Kuramoto model. This noise, in the form of a random phase perturbation at the end of each step of numerical integration, is helpful in modelling real-world physical measurements as well as realistic neural-systems.
Then, we look at where the Kuramoto model has been used in medical situations where one would like the ability to model stimulating specific neurons or parts of the system. Here we consider adding a stimulus to the model with specific application to deep-brain stimulation.
Other modifications that were not considered here include adding a time-delay consideration to the model in which the coupling effect is not applied directly to the system, but includes an in-built delay [12]. Also not considered here is a modification which allows for an effective change in the coupling constant among different oscillators in the system, such as in models of laser arrays where separate lasers may be initialised as different times [13].
Many such modifications are available for further research, and all of them pose interesting questions about future uses of the Kuramoto model.
First we consider the effect of noise on the Kuramoto model. This noise, in the form of a random phase perturbation at the end of each step of numerical integration, is helpful in modelling real-world physical measurements as well as realistic neural-systems.
Then, we look at where the Kuramoto model has been used in medical situations where one would like the ability to model stimulating specific neurons or parts of the system. Here we consider adding a stimulus to the model with specific application to deep-brain stimulation.
Other modifications that were not considered here include adding a time-delay consideration to the model in which the coupling effect is not applied directly to the system, but includes an in-built delay [12]. Also not considered here is a modification which allows for an effective change in the coupling constant among different oscillators in the system, such as in models of laser arrays where separate lasers may be initialised as different times [13].
Many such modifications are available for further research, and all of them pose interesting questions about future uses of the Kuramoto model.
