A Study of the Dynamics of a New Piecewise Smooth Map

Abstract

In this article, we have studied a [Formula: see text]D 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. [Formula: see text]. 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.

Analysis of atypical orbits in one dimensional linear piecewise-smooth discontinuous map

“…Air bubbling from a nozzle submerged in a viscous liquid is modelled by an iterating 1-D map and period adding cascades have been observed experimentally for the same [28]. A new 1-D map formed by combining logistic and tent maps behave as piecewise-smooth 1-D map, which is characterized by Lyapunov exponent and bifurcation diagrams [29]. Pulse-width modulated control of multilevel DC/DC converter resembles piecewise smooth systems.…”

Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

“…Many scholars have constructed other chaotic systems based on the tent map. In [10], a new one-dimensional piecewise chaotic map was constructed by combining a tent map with a logistic map. In [11], a class of oblique tent maps was improved, and it was proved that the chaotic system has excellent dynamic key space and practicability, making it more suitable for secure communication and other fields [12], based on the deformation of a tent map, provides piecewise linear chaotic mapping, and uses the period three theorem and topological conjugation theory to construct quadratic polynomial chaotic mapping and realize homogenization of a chaotic sequence.…”