Journal
PHYSICAL REVIEW E
Volume 93, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.93.022302
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Funding
- NSF CRCNS Grant [IIS-1430296]
- Fundacio la Caixa
- Fundacio Ferran Sunyer i Balaguer
- NIH [R01EY019493, P30 EY019005]
- NSF [IIS 1254123, 1556388]
- Salk Innovations program
- Direct For Biological Sciences
- Division Of Integrative Organismal Systems [1556388] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1254123] Funding Source: National Science Foundation
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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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