A novel chaotic map with a shifting parameter and stair-like bifurcation diagram: dynamical analysis and multistability

Abstract

In this paper, the behavior of a 1D chaotic map is proposed which includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map has a shift, and the system’s dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term makes the system have stable fixed points in some parameter intervals by increasing the bifurcation parameter. So, the bifurcation diagram of the system shows that the trend of the system’s dynamics changes in a stair shape with slope one by changing the bifurcation parameter. Due to the achieving multiple steady states in some intervals of the parameter, the proposed system is known as multistable. The multistability dynamics of the map are investigated with the help of cobweb diagrams which reveal an interesting asymmetry in repeating parts of the bifurcation diagram.