Title: Partial control of delay-coordinate maps,
Abstract: Delay-coordinate maps have been widely used recently to study nonlinear
dynamical systems, where there is only access to the time series of one of
their variables. Here, we show how the partial control method can be applied in
this kind of framework in order to prevent undesirable situations for the
system or even to reduce the variability of the observable time series
associated with it. The main advantage of this control method, is that it
allows to control delay-coordinate maps even if the control applied is smaller
than the external disturbances present in the system. To illustrate how it
works, we have applied it to three well-known models in Nonlinear Dynamics with
different delays such as the two-dimensional cubic map, the standard map and
the three-dimensional hyperchaotic Hénon map. For the first time we show here
how hyperchaotic systems can be partially controlled.