Delay-induced oscillations in Wilson and Cowan's model: an analysis of the subthalamo-pallidal feedback loop in healthy and parkinsonian subjects.

William Pasillas-Lépine 1
1 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : The model proposed by Wilson and Cowan (1972) describes the dynamics of two interacting subpopulations of excitatory and inhibitory neurons. It has been used to model neural structures like the olfactory bulb, whisker barrels, and the subthalamo-pallidal system. It is well-known that this system can exhibit an oscillatory behavior that is amplified by the presence of delays. In the absence of delays, the conditions for stability are well-known. The aim of our paper is to clarify these conditions when delays are included in the model. The first ingredient of our methods is a new necessary and sufficient condition for the existence of multiple equilibria. This condition is related to those for local asymptotic stability. In addition, a sufficient condition for global stability is also proposed. The second and main ingredient is a stability analysis of the system in the frequency-domain, based on the Nyquist criterion, that takes the four independent delays into account. The methods proposed in this paper can be applied to analyse the stability of the subthalamo-pallidal feedback loop, a deep brain structure involved in Parkinson's disease. Our stability conditions are easy to compute and characterize sharply the system's parameters for which spontaneous oscillations appear.
Complete list of metadatas

https://hal-supelec.archives-ouvertes.fr/hal-00832231
Contributor : William Pasillas-Lépine <>
Submitted on : Monday, June 10, 2013 - 1:16:22 PM
Last modification on : Thursday, October 24, 2019 - 3:08:01 PM

Links full text

Identifiers

Collections

Citation

William Pasillas-Lépine. Delay-induced oscillations in Wilson and Cowan's model: an analysis of the subthalamo-pallidal feedback loop in healthy and parkinsonian subjects.. Biological Cybernetics (Modeling), Springer Verlag, 2013, 107 (3), pp.289-308. ⟨10.1007/s00422-013-0549-3⟩. ⟨hal-00832231⟩

Share

Metrics

Record views

383