The phenomenological renormalization group (PRG) has been applied to the study of scale-invariant phenomena in neuronal data, providing evidence for critical phenomena in the brain. However, it remains unclear how reliably these observed signatures indicate genuine critical behavior, as it is not well established how close to criticality a system must be for them to emerge. Here, we rely on neuronal models with known critical points to investigate under which conditions the PRG procedure yields consistent results. We show that the PRG method detects scaling behavior in neuronal models only within a narrow vicinity of the critical point, reinforcing the interpretations drawn from PRG results in experimental data. We also demonstrate that time-binning choices can substantially affect the results and introduce a data-driven adaptive binning procedure to circumvent this issue.

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• Self-organized criticality
• Biological neural networks
• Neuronal network models
• Spiking neuron models