Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations

In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of...