title: Low-dimensional dynamics of structured random networks.
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.
authors.affiliation: Department of Neurobiology, University of Chicago, Chicago, Illinois, USA.|Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, California, USA.
authors.forename: Johnatan
authors.initials: J
authors.lastname: Aljadeff
authors.affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California, USA.
authors.forename: David
authors.initials: D
authors.lastname: Renfrew
authors.affiliation: Centre de Recerca Matemàtica, Campus de Bellaterra, Barcelona, Spain.|Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain.
authors.forename: Marina
authors.initials: M
authors.lastname: Vegué
authors.affiliation: Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, California, USA.
authors.forename: Tatyana O
authors.initials: TO
authors.lastname: Sharpee
mesh_terms: D055669:Ecological and Environmental Phenomena; D016571:Neural Networks, Computer; D009474:Neurons / Q000166:cytology; D013269:Stochastic Processes; D013569:Synapses