Collective dynamics in heterogeneous networks of neuronal cellular automata

Kaustubh Manchanda, Amitabha Bose, Ramakrishna Ramaswamy

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)111-124
Number of pages14
JournalPhysica A: Statistical Mechanics and its Applications
Volume487
DOIs
StatePublished - Dec 1 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Keywords

  • Binary mixtures
  • Boolean Lyapunov exponent
  • Discrete dynamics
  • Network motif
  • Periodic activity
  • Semi-annealed approximation

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