Optimizing charge-balanced pulse stimulation for desynchronization

TL;DR

This paper develops an optimal pulsatile control method to modulate synchronization levels in populations of oscillators, with applications in neuroscience, by deriving formulas for entropy change and validating them through simulations.

Contribution

It introduces a novel approach to optimize pulse shape and timing for desynchronization or synchronization in oscillator populations, considering realistic pulse shapes and natural frequency diversity.

Findings

Derived an expression for entropy change due to stimuli.

Validated theoretical results with numerical simulations.

Identified optimal stimulation parameters for phase control.

Abstract

Collective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it is undesirable, which calls for control techniques. In this paper, we concentrate on pulsatile control, with the goal to either increase or decrease the level of synchrony. We quantify this level by the entropy of the phase distribution. Motivated by possible applications in neuroscience, we consider pulses of a realistic shape. Exploiting the noisy Kuramoto-Winfree model, we search for the optimal pulse profile and the optimal stimulation phase. For this purpose, we derive an expression for the change of the phase distribution entropy due to the stimulus. We relate this change to the properties of individual units characterized by generally different natural frequencies and phase response curves and the population's state. We verify the general result by analyzing a two-frequency population model and demonstrating a good agreement of the theory and numerical simulations.