  Recent studies on reservoir computing essentially involve a high dimensional
dynamical system as the reservoir, which transforms and stores the input as a
higher dimensional state, for temporal and nontemporal data processing. We
demonstrate here a method to predict temporal and nontemporal tasks by
constructing virtual nodes as constituting a reservoir in reservoir computing
using a nonlinear map, namely the logistic map, and a simple finite
trigonometric series. We predict three nonlinear systems, namely Lorenz,
Rossler, and Hindmarsh-Rose, for temporal tasks and a seventh order polynomial
for nontemporal tasks with great accuracy. Also, the prediction is made in the
presence of noise and found to closely agree with the target. Remarkably, the
logistic map performs well and predicts close to the actual or target values.
The low values of the root mean square error confirm the accuracy of this
method in terms of efficiency. Our approach removes the necessity of continuous
dynamical systems for constructing the reservoir in reservoir computing.
Moreover, the accurate prediction for the three different nonlinear systems
suggests that this method can be considered a general one and can be applied to
predict many systems. Finally, we show that the method also accurately
anticipates the time series of the all the three variable of Rossler system for
the future (self prediction).
