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

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.

References in corpus (14)

• Crackling Noise
• Dynamical synapses causing self-organized criticality in neural networks
• Brain organization into resting state networks emerges at criticality on a model of the human connectome
• Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
• Self-Organized Criticality model for Brain Plasticity
• Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks
• Learning as a phenomenon occurring in a critical state
• Approximating the largest eigenvalue of network adjacency matrices
• Inhibition causes ceaseless dynamics in networks of excitable nodes
• Statistical Properties of Avalanches in Networks
• Predicting brain evoked response to external stimuli from temporal correlations of spontaneous activity
• Optimal percentage of inhibitory synapses in multi-task learning
• Critical neural networks with short and long term plasticity
• The effect of retardation in the random networks of excitable nodes embeddable in the Euclidean space