  A variety of behaviors like spatial navigation or bodily motion can be
formulated as graph traversal problems through cognitive maps. We present a
neural network model which can solve such tasks and is compatible with a broad
range of empirical findings about the mammalian neocortex and hippocampus. The
neurons and synaptic connections in the model represent structures that can
result from self-organization into a cognitive map via Hebbian learning, i.e.
into a graph in which each neuron represents a point of some abstract
task-relevant manifold and the recurrent connections encode a distance metric
on the manifold. Graph traversal problems are solved by wave-like activation
patterns which travel through the recurrent network and guide a localized peak
of activity onto a path from some starting position to a target state.
