A Study of the Dynamics of a New Piecewise Smooth Map

In this article, we have studied a 1D map, which is formed by combining the two well-known maps, i.e. the tent and the logistic maps in the unit interval, i.e. [0, 1]. The point of discontinuity of the map (known as border) denotes the transition from tent map to logistic map. The proposed map can behave as the piecewise smooth or nonsmooth map or both (depending on the behavior of the map just before and after the border) and the dynamics of the map has been studied using analytical tools and numerical simulations. Characterization has been done by primarily studying the Lyapunov exponents and the corresponding bifurcation diagrams. Some peculiar dynamics of this map have been shown numerically. Finally, a Simulink implementation of the proposed map has been demonstrated.