Time-delayed feedback in neurosystems

Abstract

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. A 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.

Amplitude and phase dynamics in oscillators with distributed-delay coupling

“…This phenomenon, named amplitude death [37], oscillator death, or 'death by delay' [39], has been demonstrated experimentally in nonlinear electronic circuits [40], in the dynamics of the slime mould Physarum polycephalum [41] and in thermo-optical oscillators linearly coupled by heat transfer [42]. Amplitude death has been subsequently studied for a number of different systems and couplings [31,[43][44][45][46][47][48][49][50][51][52].…”

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

“…By appropriate choice of the delay time, synchronization can be either enhanced or suppressed (Hauschildt et al 2006;Hövel et al in press), and this depends sensitively upon the coupling scheme (Hövel et al 2010). In the context of neural excitable systems, such timedelayed feedback loops often occur naturally due to neuro-vascular couplings, or signal propagation delays of coupled neurons (Schneider et al 2009;Schöll et al 2009a). Moreover, time-delayed feedback loops might be deliberately implemented to control neural disturbances, e.g.…”

Delay stabilization of periodic orbits in coupled oscillator systems

“…Time delays are always present in coupled systems owing to the finite signalpropagation time. These time lags give rise to complex dynamics and have been shown to play a key role in the synchronization behaviour of neural systems (Hauschildt et al 2006;Gassel et al 2007;Dahlem et al 2009;Schöll et al 2009). Coupled lasers exhibit similar phenomena to coupled neurons and have attracted much attention owing to their importance in telecommunication applications (Wünsche et al 2005;Fischer et al 2006;Klein et al 2006;Shaw et al 2006;Landsman & Schwartz 2007;Flunkert et al 2009).…”