On the role of anaxonic local neurons in the crossover to continuously varying exponents for avalanche activity

TL;DR

This paper models neuronal networks with anaxonic neurons to explore how local neuron properties influence avalanche activity, revealing a transition from universal to variable scaling exponents in activity patterns.

Contribution

It introduces a novel network model incorporating anaxonic neurons and identifies how their parameters affect criticality and scaling behavior in neural activity.

Findings

Presence of a critical line separating subcritical and supercritical regimes.

Local neuron transmission dominance leads to continuously varying exponents.

System behavior controlled by the relevance of local versus axonal transmission.

Abstract

Local anaxonic neurons with graded potential release are important ingredients of nervous systems, present in the olfactory bulb system of mammalians, in the human visual system, as well as in arthropods and nematodes. We develop a neuronal network model including both axonic and anaxonic neurons and monitor the activity tuned by the following parameters: The decay length of the graded potential in local neurons, the fraction of local neurons, the largest eigenvalue of the adjacency matrix and the range of connections of the local neurons. Tuning the fraction of local neurons, we derive the phase diagram including two transition lines: A critical line separating subcritical and supercritical regions, characterized by power law distributions of avalanche sizes and durations, and a bifurcation line. We find that the overall behavior of the system is controlled by a parameter tuning the relevance of local neuron transmission with respect to the axonal one. The statistical properties of spontaneous activity are affected by local neurons at large fractions and in the condition that the graded potential transmission dominates the axonal one. In this case the scaling properties of spontaneous activity exhibit continuously varying exponents, rather than the mean field branching model universality class.