Detecting Unstable Sets in an Estimated Parameter Space for the H ' enon Map

A method has been proposed for reconstructing bifurcation diagrams by estimating the parameter space from only time-series data sets. Here, the time-series data sets are generated from an unknown sys-tem with different parameter values and we detect unstable sets in an estimated parameter space for the He ' non map. In this way, chaos in the unknown system can be controlled to stay as an unstable set. With this method, we can identify both the stable and unstable sets even when the parameter values change. Results of numerical exper-iments are presented for detection of unstable sets of various cycles in the estimated parameter space.(c) 2023 L&H Scientific Publishing, LLC. All rights reserved.