Lengths of Attractors and Transients in Neuronal Networks with Random Connectivities
| Autor: | Winfried Just, Sungwoo Ahn |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Random graph
Discrete mathematics Phase transition Quantitative Biology::Neurons and Cognition General Mathematics Dynamical Systems (math.DS) 01 natural sciences 05C20 05C80 37F20 92C20 92C42 010305 fluids & plasmas Connection (mathematics) Erdős–Rényi model Combinatorics Complex dynamics Boolean network 0103 physical sciences Attractor FOS: Mathematics Mathematics - Dynamical Systems 010306 general physics Focus (optics) Mathematics |
| Zdroj: | SIAM Journal on Discrete Mathematics. 30:912-933 |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/140996045 |
| 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: | OpenAIRE |
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