# Generation of theta oscillations by weakly coupled neural oscillators in the presence of noise

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## Abstract

Neuronal oscillations are a robust phenomenon occurring in a variety of brain regions despite considerable amounts of noise. In this article classical phase-response theory is generalized to the case of noisy weak-coupling regimes by deriving an iterated map for the asynchrony of spikes in an oscillation cycle. Two criteria are introduced to check the validity of our approximations: One criterion tests the assumption that all neurons fire exactly once per cycle, the other criterion tests for linearity. The framework is applied to stellate cells of the medial entorhinal cortex layer II. We find that rhythmogenesis is more robust in the case of excitatory noise as compared to inhibitory noise. It is shown that a network of stellate cells can also act as a generator of theta if the neurons are connected via a fast-oscillating network of inhibitory interneurons.

## Keywords

Phase-response theory Synaptic noise Theta rhythm Stellate cell## Notes

### Acknowledgments

The authors thank Jan Benda and Roland Schaette for insightful comments on the manuscript and are grateful to Andreas Herz, Richard Kempter for ongoing support and Dietmar Schmitz for support and discussions on stellate cell physiology. This work has been supported by the Berliner NaFöG grant (MB), and the Deutsche Forschungsgemeinschaft (DFG) via SFB 618 Theoretical Biology (MB & CL) as well as via the Emmy-Noether grant (Ke 788/1-3,4) to Richard Kempter (CL) and the Bundesministerium für Bildung und Forschung (Bernstein Center for Computational Neuroscience Berlin, 01GQ0410).

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