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Journal of Applied Nonlinear Dynamics 12(3) (2023) 579-589 | DOI:10.5890/JAND.2023.09.011

Yoshitaka Itoh

Department of Electrical and Electronic Engineering, Hokkaido University of Science, 7-Jo 15-4-1 Maeda, Teine, Sapporo, Hokkaido 006-8585, Japan

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Abstract

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 H{\'e}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 experiments are presented for detection of unstable sets of various cycles in the estimated parameter space.

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