Journal of Computational Neuroscience

, Volume 44, Issue 3, pp 363–378 | Cite as

Phase model-based neuron stabilization into arbitrary clusters

  • Timothy D. Matchen
  • Jeff Moehlis


Deep brain stimulation (DBS) is a common method of combating pathological conditions associated with Parkinson’s disease, Tourette syndrome, essential tremor, and other disorders, but whose mechanisms are not fully understood. One hypothesis, supported experimentally, is that some symptoms of these disorders are associated with pathological synchronization of neurons in the basal ganglia and thalamus. For this reason, there has been interest in recent years in finding efficient ways to desynchronize neurons that are both fast-acting and low-power. Recent results on coordinated reset and periodically forced oscillators suggest that forming distinct clusters of neurons may prove to be more effective than achieving complete desynchronization, in particular by promoting plasticity effects that might persist after stimulation is turned off. Current proposed methods for achieving clustering frequently require either multiple input sources or precomputing the control signal. We propose here a control strategy for clustering, based on an analysis of the reduced phase model for a set of identical neurons, that allows for real-time, single-input control of a population of neurons with low-amplitude, low total energy signals. After demonstrating its effectiveness on phase models, we apply it to full state models to demonstrate its validity. We also discuss the effects of coupling on the efficacy of the strategy proposed and demonstrate that the clustering can still be accomplished in the presence of weak to moderate electrotonic coupling.


Coupling Neural oscillators Parkinson’s Clustering Phase models 



Support for this work by National Science Foundation Grants No. NSF-1264535/1631170 and NSF-1635542 is gratefully acknowledged.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA

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