Self-organized structures in networks with spike-timing dependent plasticity
(STDP) are likely to play a central role for information processing in the
brain. In the present study we derive a reaction-diffusion-like formalism for
plastic feed-forward networks of nonlinear rate neurons with a correlation
sensitive learning rule inspired by and being qualitatively similar to STDP.
After obtaining equations that describe the change of the spatial shape of the
signal from layer to layer, we derive a criterion for the non-linearity
necessary to obtain stable dynamics for arbitrary input. We classify the
possible scenarios of signal evolution and find that close to the transition to
the unstable regime meta-stable solutions appear. The form of these dissipative
solitons is determined analytically and the evolution and interaction of
several such coexistent objects is investigated
