Oscillation Onset in Neural Delayed Feedback

This paper studies dynamical aspects of neural systems with delayed negative feedback modelled by nonlinear delay-differential equations. These systems undergo a Hopf bifurcation from a stable fixed point to a stable limit cycle oscillation as certain parameters are varied. It is shown that their frequency of oscillation is robust to parameter variations and noisy fluctuations, a property that makes these systems good candidates for pacemakers. The onset of oscillation is postponed by both additive and parametric noise in the sense that the state variable spends more time near the fixed point than it would in the absence of noise. This is also the case when noise affects the delayed variable, i.e. when the system has a faulty memory. Finally, it is shown that a distribution of delays (rather than a fixed delay) also stabilizes the fixed point solution.