• network basal ganglia python Kuramoto oscillators

In this work it is shown that modeling the Basal Ganglia system with three populations of Kuramoto oscillators - in which one oscillator comprises neurons from several nuclei in the network, emulating the traveling path of a signal - leads to some limitation to what information can be gathered using only analytical tools. The first result involves the formulation of one population’s synchronization parameter when the other two have already obtained a highly synchronized state showing that it depends on the coupling constants between said population and the remaining ones. When only one population has obtained such a state, the synchronization parameters of the other two populations have been plotted showing that an increase in the coupling constants amongst these leads to a shrinkage of the plotted surfaces limiting the set of acceptable values. The system has been simulated using the tools provided by Python 3, it is shown that there exist a meta-stable state in which the synchronization parameter of a population oscillates from a state of higher synchronization to a state of lower synchronization, this meta-stable state is lost when the coupling constants are furtherly increased. The insight here is that the meta-stable state represents a general physiological state which is lost when the amount of dopaminergic projections from the Substantia Nigra to the Striatum decreases, this leading to an increase of the coupling between the oscillators in the modeled system.