Self-calming of a random network of dendritic neurons

A network of neurons with dendritic dynamics is analyzed in this paper. Two stable regimes of the complete network can coexist under continuous weak stimulation: the oscillatory synchronized regime and the quiet regime, where all neurons stop firing completely. It is shown that a single control pulse can calm a single neuron as well as the whole network, and the network stays in the quiet regime as long as the weak stimulation is turned on. It is also demonstrated that the same control technique can be effectively used to calm a random Erdös–Renyi network of dendritic neurons. Moreover, it appears that the random network of dendritic neurons can evolve into the quiet regime without applying any external pulse-based control techniques.