Collective dynamics in heterogeneous networks of neuronal cellular automata

Document Type

Article

Publication Date

12-1-2017

Abstract

We examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata. Each automaton has b active states, a single silent state and r−b−1 refractory states, and can show ‘spiking’ or ‘bursting’ behavior, depending on the values of b. We show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of Erdõs–Rényi graphs as a function of edge probability. Different forms of heterogeneity allow distinct structural phase transitions to become relevant. We also show that the dynamics on the network can be described by a semi-annealed process and, as a result, can be related to the Boolean Lyapunov exponent.

Identifier

85022174828 (Scopus)

Publication Title

Physica A Statistical Mechanics and Its Applications

External Full Text Location

https://doi.org/10.1016/j.physa.2017.06.021

ISSN

03784371

First Page

111

Last Page

124

Volume

487

Grant

DMS-112291

Fund Ref

National Science Foundation

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