Bifurcation Analysis of a Sparse Neural Network with Cubic Topology

Autor:	Anna Cattani, Diego Fasoli, Stefano Panzeri
Rok vydání:	2017
Předmět:	Formalism (philosophy of mathematics) Neural activity Bifurcation analysis Quantitative Biology::Neurons and Cognition Artificial neural network Computer science Topology Network model
Zdroj:	Mathematical and Theoretical Neuroscience ISBN: 9783319682969
DOI:	10.1007/978-3-319-68297-6_5
Popis:	We study analytically the changes of dynamics of a firing-rate network model with cubic topology. The present study is performed by extending to this sparse network a formalism we previously developed for the bifurcation analysis of fully-connected circuits. In particular we prove that, unlike the fully-connected model, in the cubic network the neural activity may undergo spontaneous symmetry-breaking even if the network is composed exclusively of excitatory neurons. Moreover, while in the fully-connected topology the symmetry-breaking occurs through pitchfork bifurcations, in the excitatory cubic network it occurs through complex branching-point bifurcations with five branches. These results lead to the conclusion that the sparseness of the synaptic connections may increase the complexity of dynamics compared to dense networks.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::890c5dcabfa82fa86f18555b82d5bd3e https://doi.org/10.1007/978-3-319-68297-6_5 Zobrazit plný text záznamu