Criteria_for_robustness_of_heteroclinic_cycles_in_neural.pdf (1007.55 kB)
Criteria for robustness of heteroclinic cycles in neural microcircuits
journal contribution
posted on 2023-06-08, 09:48 authored by Peter Ashwin, Thomas NowotnyThomas Nowotny, Özkan KarabacakWe 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.
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Publication status
- Published
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- Published version
Journal
Journal of Mathematical NeuroscienceISSN
0929-5313Publisher
Springer VerlagExternal DOI
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13Volume
1Page range
1-18Department affiliated with
- Informatics Publications
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- Yes
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- Yes
Legacy Posted Date
2012-05-30First Open Access (FOA) Date
2016-03-22First Compliant Deposit (FCD) Date
2016-11-10Usage metrics
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