Desynchronization of systems of coupled Hindmarsh-Rose oscillators

TL;DR

This paper explores how variable delay feedback can enhance desynchronization in large systems of coupled Hindmarsh-Rose neural oscillators, potentially improving control of pathological neural rhythms.

Contribution

It introduces a variable delay feedback mechanism that broadens the parameter range for effective desynchronization in coupled HR oscillators.

Findings

Variable delay feedback achieves more robust desynchronization.

Desynchronization is effective over a wider parameter range.

The method enhances the suppression of synchronized neural activity.

Abstract

It is widely assumed that neural activity related to synchronous rhythms of large portions of neurons in specific locations of the brain is responsible for the pathology manifested in patients' uncontrolled tremor and other similar diseases. To model such systems Hindmarsh-Rose (HR) oscillators are considered as appropriate as they mimic the qualitative behaviour of neuronal firing. Here we consider a large number of identical HR-oscillators interacting through the mean field created by the corresponding components of all oscillators. Introducing additional coupling by feedback of Pyragas type, proportional to the difference between the current value of the mean-field and its value some time in the past, Rosenblum and Pikovsky (Phys. Rev. E 70, 041904, 2004) demonstrated that the desirable desynchronization could be achieved with appropriate set of parameters for the system. Following our experience with stabilization of unstable steady states in dynamical systems, we show that by introducing a variable delay, desynchronization is obtainable for much wider range of parameters and that at the same time it becomes more pronounced.