# Berlin 2018 – wissenschaftliches Programm

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# BP: Fachverband Biologische Physik

## BP 34: Neuroscience

### BP 34.2: Vortrag

### Donnerstag, 15. März 2018, 15:30–15:45, H 1058

**Spike rate models derived from recurrent networks of adaptive neurons** — •Moritz Augustin, Josef Ladenbauer, Fabian Baumann, and Klaus Obermayer — Technische Universität Berlin, Germany

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in large-scale brain network models.