Bifurcation Analysis of a Class of Generalized Hénon Maps with Hidden Dynamics

Although continuous systems such as the Chua circuit are known as systems with hidden attractors, hidden attractors also exist in classical discrete maps, such as a generalized Hénon map. A hidden attractor is an attractor that does not overlap with its own attracting region in its vicinity, which makes it difficult to visualize. In this paper, a local bifurcation analysis method for discrete maps is described, and the bifurcation analysis of the generalized Hénon map is performed using the method. The bifurcation structure, as the parameters are changed, shows a certain law, and the interesting Neimark-Sacker bifurcation and period-doubling bifurcation are confirmed to occur simultaneously. It was also found that the hidden attractors exist in the rectangular characteristic chaotic regions, and they appear relatively frequently near the window of chaos.

This is the peer reviewed version of the following article: Amoh, S., Zhang, X., Chen, G. and Ueta, T. (2021), Bifurcation analysis of a class of generalized Hénon maps with hidden dynamics. IEEJ Trans Elec Electron Eng, 16: 1456-1462., which has been published in final form at https://doi.org/10.1002/tee.23480. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.