title: Equation-free analysis of spike-timing-dependent plasticity.
abstract: Spike-timing-dependent plasticity is the process by which the strengths of connections between neurons are modified as a result of the precise timing of the action potentials fired by the neurons. We consider a model consisting of one integrate-and-fire neuron receiving excitatory inputs from a large number-here, 1000-of Poisson neurons whose synapses are plastic. When correlations are introduced between the firing times of these input neurons, the distribution of synaptic strengths shows interesting, and apparently low-dimensional, dynamical behaviour. This behaviour is analysed in two different parameter regimes using equation-free techniques, which bypass the explicit derivation of the relevant low-dimensional dynamical system. We demonstrate both coarse projective integration (which speeds up the time integration of a dynamical system) and the use of recently developed data mining techniques to identify the appropriate low-dimensional description of the complex dynamical systems in our model.
authors.affiliation: Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand. c.r.laing@massey.ac.nz.
authors.forename: Carlo R
authors.initials: CR
authors.lastname: Laing
authors.affiliation: Department of Chemical and Biological Engineering, Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA. yannis@princeton.edu.
authors.forename: Ioannis G
authors.initials: IG
authors.lastname: Kevrekidis
mesh_terms: D000200:Action Potentials; D008962:Models, Theoretical; D009473:Neuronal Plasticity
keywords: Equation-free; Model reduction; Neuronal network; Spike-timing-dependent plasticity