Criteria for robustness of heteroclinic cycles in neural microcircuits

Ashwin, Peter, Nowotny, Thomas and Karabacak, Özkan (2011) Criteria for robustness of heteroclinic cycles in neural microcircuits. Journal of Mathematical Neuroscience, 1 (13). pp. 1-18. ISSN 0929-5313

[img]
Preview
PDF - Published Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview

Abstract

We introduce a test for robustness of heteroclinic cycles that appear in
neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles
(RHCs) can appear as robust attractors in Lotka-Volterra-type winnerless competition
(WLC) models as well as in more general coupled and/or symmetric systems. It has
been previously suggested that RHCs may be relevant to a range of neural activities,
from encoding and binding to spatio-temporal sequence generation.
The robustness or otherwise of such cycles depends both on the coupling structure
and the internal structure of the neurons. We verify that robust heteroclinic cycles
can appear in systems of three identical cells, but only if we require perturbations to
preserve some invariant subspaces for the individual cells. On the other hand, heteroclinic
attractors can appear robustly in systems of four or more identical cells for
some symmetric coupling patterns, without restriction on the internal dynamics of
the cells.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
Depositing User: Thomas Nowotny
Date Deposited: 30 May 2012 09:27
Last Modified: 07 Mar 2017 04:25
URI: http://sro.sussex.ac.uk/id/eprint/30959

View download statistics for this item

📧 Request an update