1. A method, comprising: determining synaptic weights for synapse devices configured for connecting axons of source electronic neurons to dendrites of target electronic neurons in a spiking neuronal network, wherein the synaptic weights are based on learning rules for the neuronal network, such that a synaptic weight for a synapse device determines the effect of a spiking source electronic neuron on a target electronic neuron connected via that synapse device; and dynamically maintaining total synaptic weights in the spiking neuronal network at a predetermined range for neural network stability.