Lengths of attractors and transients in neuronal networks with random connectivities

Autor:	Just, Winfried, Ahn, Sungwoo
Rok vydání:	2014
Předmět:	Mathematics - Dynamical Systems 05C20 05C80 37F20 92C20 92C42
Druh dokumentu:	Working Paper
Popis:	We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically derive scaling laws for the average lengths of the attractors and transients under certain restrictions on the intrinsic parameters of the neurons, that is, their refractory periods and firing thresholds. In contrast to earlier results that were reported in \cite{TAWJ}, here we focus on the connection probabilities near the phase transition where the most complex dynamics is expected to occur. Comment: 39 pages with 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1404.5536 Zobrazit plný text záznamu View this record from Arxiv