---
abstract: 'The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns, or amplitude death.'
author:
- 'E. Schöll'
- 'G. Hiller'
- 'P. H[ö]{}vel'
- 'M. A. Dahlem'
title: 'Time-Delayed Feedback in Neurosystems'
---

Introduction
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Control of unstable or irregular states of nonlinear dynamic systems is a central issue of current research [@SCH07]. A particularly simple and efficient control scheme is time-delayed feedback which occurs naturally in a number of biological systems including neural networks where both propagation delays of electrical signals connecting different neurons and local neurovascular couplings lead to time delays [@HAK06; @WIL99; @GER02]. Moreover, time-delayed feedback loops might be deliberately implemented to control 