It is possible to add a further term to the Kuramoto model that can model stimulation to the system from an external source. such modification has been made in considering uses of the Kuramoto model in research of deep brain stimulation [11]. There are a variety of methods by which one can add stimulation, one such method is;
The main application of this technique is in research to discover a technique that could be applied in a real-world situation, such as to stimulate deep brain matter of patients with Parkinson's diseases for instance, where a 'hard reset' using abrupt and sudden charge could damage a patient's brain.
Where Xi(t) is either 0 or 1 depending on whether stimulation is being applied at time t. As the impact of an electrical stimulus upon a neuron depends on it's current phase, we can model this with a 2π-periodic time-independent function [10] such as S(θi)=I cos(θi), where I is the intensity of the stimulus. The other variables are as the Kuramoto Model with Noise.Introducing this form of 'soft resetting' allows one to desynchronise the system without using abrupt and fixed input to the system, or without modifying constants in the system during simulation. By repeatedly applying this form of 'soft resetting' at regular intervals, one can keep the system in an unsynchronised state.
The main application of this technique is in research to discover a technique that could be applied in a real-world situation, such as to stimulate deep brain matter of patients with Parkinson's diseases for instance, where a 'hard reset' using abrupt and sudden charge could damage a patient's brain.
