# A Study of the Dynamics of a new Piecewise Smooth Map

## TL;DR

This paper investigates a novel 1D piecewise map combining tent and logistic maps, analyzing its complex dynamics through Lyapunov spectra, bifurcation diagrams, and numerical simulations, including a Simulink implementation.

## Contribution

It introduces a new piecewise smooth map, explores its dynamics analytically and numerically, and demonstrates its implementation in Simulink.

## Key findings

- The map exhibits both smooth and non-smooth behaviors.
- Complex bifurcation structures are observed.
- Unique dynamical phenomena are numerically demonstrated.

## Abstract

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 proposed map can behave as the piecewise smooth or non-smooth maps (depending on the behaviour of the map just before and after the border) and then the dynamics of the map has been studied using analytical tools and numerical simulations. Characterization has been done by primarily studying the Lyapunov spectra 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.