Absence of supersensitivity to small input signals in generalized on--off systems

It has recently been shown that nonlinear skew product dynamical systems with invariant subspaces which are capable of displaying on-off intermittency can show supersensitivity to small input signals. Here we show that this supersensitivity is absent for more general dynamical systems with non-skew product structure, capable of displaying a generalized form of on-off intermittency, and is therefore in this sense fragile. This absence of supersensitivity is of importance in view of the fact that dynamical systems are generically expected to be of non-skew product nature.