Pulse desynchronization of neural populations by targeting the centroid of the limit cycle in phase space

The synchronized activity of neuronal populations can lead to pathological over-synchronization in conditions such as epilepsy and Parkinson disease. Such states can be desynchronized by brief electrical pulses. But when the underlying oscillating system is not known, as in most practical applications, to determine the specific times and intensities of pulses used for desynchronizaton is a difficult inverse problem. Here we propose a desynchronization scheme for neuronal models of bi-variate neural activity, with possible applications in the medical setting. Our main argument is the existence of a peculiar point in the phase space of the system, the centroid, that is both easy to calculate and robust under changes in the coupling constant. This important target point can be used in a control procedure because it lies in the region of minimal return times of the system.

Source: arXiv:2603.12878v1 - http://arxiv.org/abs/2603.12878v1 PDF: https://arxiv.org/pdf/2603.12878v1 Original Link: http://arxiv.org/abs/2603.12878v1