Detecting Unstable Sets in an Estimated Parameter Space for the Hénon Map - Itoh, Yoshitaka (Journal of Applied Nonlinear Dynamics, 2026)
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 system with different parameter values and we detect unstable sets in an estimated parameter space for the Hénon 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 experiments are presented for detection of unstable sets of various cycles in the estimated parameter space.