Using the delayed coordinate vectors of a music signal and a fixed
control sequence we train the network to give a vector valued
prediction of the following 
time samples. To ensure a
discriminating control input, we chose a control sequence linear
increasing with the sample time. After training we initialize the
network input with the first input vector 
of the
time series and iterate the network function shifting the network
input and using the latest output unit to complete the new input. The
control input sequence may be copied from the training phase to
resynthesize the training signal or may be varied to get
a variation of the musical sound.
The question that arises in this context is the question of stability.
As we will see in the example, the neural models are stable for
selected parameters 
and 
. Due to the embedding of the
attractor, however, this stability, which depends on its neighborhood,
is not guaranteed and it may be the case for other time series, that
there are no parameters for stable models. A method for controlling
the stability of the models is subject of further research.