Error growth in the time-dependent logistic equation

In order to analyze the impact of time-dependent forcings in the behavior of the error growth we study a non-autonomous logistic equation. The sign of the Lyapunov exponent of the system depends on the frequency of the forcing. For finite initial errors, at initial stages the growth occurs in sub- and super-exponential ways, and finally oscillates around the saturation level. The form of the errors of the autonomous case is recovered when we average over many initial times, showing the importance of this parameter in time-dependent systems.