title: Reaction-diffusion-like formalism for plastic neural networks reveals dissipative solitons at criticality.
abstract: Self-organized structures in networks with spike-timing dependent synaptic 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-based model 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 nonlinearity 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 metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
authors.affiliation: Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6), Jülich Research Centre and JARA, Jülich, Germany.
authors.forename: Dmytro
authors.initials: D
authors.lastname: Grytskyy
authors.affiliation: Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6), Jülich Research Centre and JARA, Jülich, Germany.|Medical Faculty, RWTH Aachen University, Germany.|Department of Physics, Faculty 1, RWTH Aachen University, 52074 Aachen, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Diesmann
authors.affiliation: Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6), Jülich Research Centre and JARA, Jülich, Germany.|Department of Physics, Faculty 1, RWTH Aachen University, 52074 Aachen, Germany.
authors.forename: Moritz
authors.initials: M
authors.lastname: Helias
mesh_terms: D000200:Action Potentials; D003198:Computer Simulation; D007858:Learning; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009473:Neuronal Plasticity