Influence of Noise, Variability, and Time-delayed Feedback on Networks: Dynamics of Neural Networks

In this thesis, the influence of noise, variability, and time-delayed feedback on the dynamics of nets of neural elements is investigated. The dynamics of the single elements is given by the FitzHugh-Nagumo, the Hodgkin-Huxley, or the reduced Hodgkin-Huxley equations. After some theoretical basics, the results are presented. For oscillatory nets, it is shown that time-delayed feedback can suppress oscillations and thereby excitable net dynamics is induced. In subexcitable nets, time-delayed feedback can support the propagation of wave fronts and thereby pattern formation. This effect is studied in detail for wave fronts, which are either induced by special initial conditions, by noise, or by variability. For bistable nets, it is shown that both multiplicative noise and multiplicative variability have a systematic influence on the net dynamics. Considering an external signal, the response of the net is optimal for intermediate values of the additive and the multiplicative variability strength (doubly variability-induced resonance). Moreover, the response of the net to the external signal can further be enhanced applying time-delayed feedback with appropriately chosen delay times.