Suppression of global oscillations via time-delayed feedback in a net of neural elements

The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is investigated. We show that the global oscillation of the net can be suppressed (amplitude death) and excitable network dynamics can be restored via time-delayed feedback for a properly chosen delay time. We investigate the influence of local and global feedback and the dependence of the amplitude death regime on the parameters of the feedback signal. Furthermore the influence of the coupling strength on the transition from the global oscillation to excitable network dynamics is studied. Starting with a net, whose global oscillation is suppressed, weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.