
Negative feedback systems 135
of different values of the time delay τ. Fig. 4.13 reports the time res po nse
of the nonlinear system for
˜
d = ¯x
2
/8, T = 10 h (for better visualisation, the
pulse perturbation is applied at time t = 10 h): it is clearly visible that the
analysis conducted on the linearised system holds also for the nonlinear s ys-
tem, at least for a moderate perturbation of the state from the equilibrium
condition. For τ < 0.46 the oscillations induced by the perturbation dampen
out, for τ = 0.46 they exhibit a constant amplitude, whereas for τ > 0.46 the
oscillation is unstable. Note that in the latter case the oscillation amplitude