Complex network-based multistep forecasting model for hyperchaotic time series

We present a method for predicting hyperchaotic time series using a complex network-based forecasting model. We first construct a network from a given time series, which serves as a coarse-grained representation of the underlying attractor. This network facilitates multistep forecasting by capturing the local nonlinearity of the dynamics and offers superior accuracy over more extended periods than traditional methods. The network is formed by converting the patterns of local oscillations into sequences of numerical symbols, which are then used to create nodes and edges in a network, capturing the system's dynamical behavior at a reduced resolution. The network allows predictions up to several steps ahead without the exponential error increase usually associated with linear first-order methods. The improved predictions result from the unique ability of the network to collect identical pattern transitions in the orbit dynamics into a system of neighborhoods in the network. The effectiveness of this approach is demonstrated through its application to several high-dimensional hyperchaotic systems, where it outperforms both the linear first-order and other network-based methods in terms of prediction accuracy and horizon. Besides enhancing the predictability of chaotic systems, this methodology also outlines a procedure to develop a discrete model flow within an attractor.