  The response of dynamical systems to varying conditions and disturbances is a
fundamental aspect of their analysis. In spatially extended systems,
particularly in pattern-forming systems, there are many possible responses,
including critical transitions, gradual transitions and locally confined
responses. Here, we use the context of vegetation dynamics in drylands in order
to study the response of pattern-forming ecosystems to oscillating
precipitation and local disturbances. We focus on two precipitation ranges, a
bistability range of bare soil with a patterned vegetation state, and a
bistability range of uniform vegetation with a patterned vegetation state. In
these ranges, there are many different stable states, which allow for both
abrupt and gradual transitions between the system states to occur. We find that
large amplitude oscillations of the precipitation rate can lead to a collapse
of the vegetation in one range, while in the other range, they result in the
convergence to a patterned state with a preferred wavelength. In addition, we
show that a series of local disturbances results in the collapse of the
vegetation in one range, while it drives the system toward fluctuations around
a finite average biomass in the other range. Moreover, it is shown that under
certain conditions, local disturbances can actually increase the overall
vegetation density. These significant differences in the system response are
attributed to the existence of localized states in one of the bistability
ranges.
