Abstract
In the wide literature on the brain and neural network dynamics the notion of criticality is being adopted by an increasing number of researchers, with no general agreement on its theoretical definition, but with consensus that criticality makes the brain very sensitive to external stimuli. We adopt the complexity matching principle that the maximal efficiency of communication between two complex networks is realized when both of them are at criticality. We use this principle to establish the value of the neuronal interaction strength at which criticality occurs, yielding a perfect agreement with the adoption of temporal complexity as criticality indicator. The emergence of a scale-free distribution of avalanche size is proved to occur in a supercritical regime. We use an integrate-and-fire model where the randomness of each neuron is only due to the random choice of a new initial condition after firing. The new model shares with that proposed by Izikevich the property of generating excessive periodicity, and with it the annihilation of temporal complexity at supercritical values of the interaction strength. We find that the concentration of inhibitory links can be used as a control parameter and that for a sufficiently large concentration of inhibitory links criticality is recovered again. Finally, we show that the response of a neural network at criticality to a harmonic stimulus is very weak, in accordance with the complexity matching principle.
Highlights
The problem of the response of a complex system to external stimuli is of central interest for brain dynamics
We find that the power law1.5 emerges at about k = 5 · 10−7, which is a value significantly larger than 3.3 · 107 signaling the emergence of temporal complexity
Werner [32] refers himself to phase transitions in physics, as illustrated by renormalization group theory, thereby implying that the brain lives in a condition between local and long-range correlation
Summary
In the wide literature on the brain and neural network dynamics the notion of criticality is being adoplicence. We adopt the attribution to the author complexity matching principle that the maximal efficiency of communication between two complex (s) and the title of the work, journal citation and networks is realized when both of them are at criticality. We use this principle to establish the value of DOI. The neuronal interaction strength at which criticality occurs, yielding a perfect agreement with the adoption of temporal complexity as criticality indicator. The new model shares with that proposed by Izikevich the property of generating excessive periodicity, and with it the annihilation of temporal complexity at supercritical values of the interaction strength. We show that the response of a neural network at criticality to a harmonic stimulus is very weak, in accordance with the complexity matching principle
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