Seiya Amoh, Xu Zhang, Guanrong Chen, Tetsushi Ueta, Bifurcation Analysis of a Class of Generalized Henon Maps with Hidden Dynamics, The Institute of Electrical Engineers of Japan, IEEJ Trans. Fundamentals and Materials, Nov. 2021.
Abstract: 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 Henon 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 Henon 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.