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Criteria for robustness of heteroclinic cycles in neural microcircuits

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posted on 2023-06-08, 09:48 authored by Peter Ashwin, Thomas NowotnyThomas Nowotny, Özkan Karabacak
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Mathematical Neuroscience

ISSN

0929-5313

Publisher

Springer Verlag

Issue

13

Volume

1

Page range

1-18

Department affiliated with

  • Informatics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2012-05-30

First Open Access (FOA) Date

2016-03-22

First Compliant Deposit (FCD) Date

2016-11-10

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