ArticlePhysical review. E2016
Low-dimensional dynamics of structured random networks.
Article in Physical review. E, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- Strong and localized recurrence controls the dimensionality of neural activity across brain areas.Nature neuroscience · 2026Article
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- Relating local connectivity and global dynamics in recurrent excitatory-inhibitory networks.PLoS computational biology · 2023Article
- Input correlations impede suppression of chaos and learning in balanced firing-rate networks.PLoS computational biology · 2022Article
- Small, correlated changes in synaptic connectivity may facilitate rapid motor learning.Nature communications · 2022Article
- Article
- Neural manifold under plasticity in a goal driven learning behaviour.PLoS computational biology · 2021Article
- Propagation of orientation selectivity in a spiking network model of layered primary visual cortex.PLoS computational biology · 2019Article
- Specific excitatory connectivity for feature integration in mouse primary visual cortex.PLoS computational biology · 2017Article
- Rat Prefrontal Cortex Inactivations during Decision Making Are Explained by Bistable Attractor Dynamics.Neural computation · 2017Article
- Linking structure and activity in nonlinear spiking networks.PLoS computational biology · 2017Article
- Intrinsically-generated fluctuating activity in excitatory-inhibitory networks.PLoS computational biology · 2017Article
- Eigenvalue spectra of large correlated random matrices.Physical review. E · 2016Article
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Authors and funding
4 authors.
Funding
Abstract
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, and T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network connectivity structure and its low-dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and postsynaptic neurons through a sufficiently smooth function g of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive as a function of g. Above the critical point, although unit activation levels are chaotic, their autocorrelation functions are restricted to a low-dimensional subspace. This provides a direct link between the network's structure and some of its functional characteristics. We discuss example applications of the general results to neuroscience where we derive the support of the spectrum of connectivity matrices with heterogeneous and possibly correlated degree distributions, and to ecology where we study the stability of the cascade model for food web structure.
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