This paper, An Adaptive Spiking Neural Network with Hebbian Learning, specifically addresses the creation of new neurons and synapses. From the introduction:
Traditional rate-based neural networks and the newer spiking neural networks have been shown to be very effective for some tasks, but they have problems with long term learning and "catastrophic forgetting." Once a network is trained to perform some task, it is difficult to adapt it to new applications. To do this properly, one can mimic processes that occur in the human brain: neurogenesis and synaptogenesis, or the birth and death of both neurons and synapses. To be effective, however, this must be accomplished while maintaining the current memories.
If you do some searching on google with the keywords 'neurogenesis artificial neural networks', or similar, you will find more articles. There is also this similar question at cogsci.stackexchange.com.