Laing Carlo R, Kevrekidis Ioannis G
Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand.
Department of Chemical and Biological Engineering, Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA.
Biol Cybern. 2015 Dec;109(6):701-14. doi: 10.1007/s00422-015-0668-0. Epub 2015 Nov 17.
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.
