Dynamics of a subthalamic nucleus-globus palidus network with three delays

B. Rahman, Y. N. Kyrychko, K. B. Blyuss, S. J. Hogan

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)

Abstract

This paper analyses a model of the subthalamic nucleus (STN)-globus palidus (GP) network with three different transmission delays. A time-shift transformation reduces the model to a system with two time delays, for which the existence of a unique steady state is established. Conditions for stability of the steady state are derived in terms of system parameters and time delays. Numerical stability analysis is performed using traceDDE to investigate different dynamical regimes in the STN-GP model, and to obtain critical stability boundaries separating stable (healthy) and oscillatory (Parkinsonian-like) neural firing. Direct numerical simulations of the fully nonlinear system are performed to confirm analytical findings, and to illustrate different dynamical behaviours of the system.

Original languageEnglish
Pages (from-to)294-299
Number of pages6
JournalIFAC-PapersOnLine
Volume51
Issue number14
Early online date29 Aug 2018
DOIs
Publication statusE-pub ahead of print - 29 Aug 2018

Keywords

  • Stability Analysis
  • Subthalamic Nucleus (STN)-Globus Palidus (GP)
  • Time Delays

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