2025/06/27 by Joaquín Almeira, Daniel A. Mártin, Almeira, Joaquin +5
Computer Science · Neuroscience · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2506.22629
openalex publication_date 2025/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the scaling behaviour of the fluctuation susceptibility associated with the average activation in the Greenberg-Hastings neural network model and its relation to microscopic spontaneous activation. We found that, as the spontaneous activation probability tends to zero, a clear finite size scaling behaviour in the susceptibility emerges, characterized by critical exponents which follow already known scaling laws. This shows that the spontaneous activation probability plays the role of an external field conjugated to the order parameter of the dynamical activation transition. The roles of different kinds of activation mechanisms around the different dynamical phase transitions exhibited by the model are characterized numerically and using a mean field approximation.