1. A method, comprising: determining synaptic weights for electronic synapses 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 an electronic synapse determines the effect of a spiking source electronic neuron on a target electronic neuron connected via that electronic synapse; and dynamically maintaining total synaptic weights in the spiking neuronal network at a predetermined range for neural network stability by adjusting a synaptic weight for at least one electronic synapse; wherein, for an electronic synapse connected to an electronic neuron, a synaptic weight for said electronic synapse is adjusted based on a total synaptic weight for electronic synapses connected to said electronic neuron.