ArticleBiological cybernetics2022
Codimension-2 parameter space structure of continuous-time recurrent neural networks.
Article in Biological cybernetics, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- A minimal physiological model of perceptual suppression and breakthrough in visual rivalry.Journal of vision · 2026Article
- Article
- Flexible multitask computation in recurrent networks utilizes shared dynamical motifs.Nature neuroscience · 2024Article
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Abstract
If we are ever to move beyond the study of isolated special cases in theoretical neuroscience, we need to develop more general theories of neural circuits over a given neural model. The present paper considers this challenge in the context of continuous-time recurrent neural networks (CTRNNs), a simple but dynamically universal model that has been widely utilized in both computational neuroscience and neural networks. Here, we extend previous work on the parameter space structure of codimension-1 local bifurcations in CTRNNs to include codimension-2 local bifurcation manifolds. Specifically, we derive the necessary conditions for all generic local codimension-2 bifurcations for general CTRNNs, specialize these conditions to circuits containing from one to four neurons, illustrate in full detail the application of these conditions to example circuits, derive closed-form expressions for these bifurcation manifolds where possible, and demonstrate how this analysis allows us to find and trace several global codimension-1 bifurcation manifolds that originate from the codimension-2 bifurcations.
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