The quadratic map and its temporal and spectral properties

TL;DR

This paper numerically investigates the temporal and spectral characteristics of a quadratic map with non-linearity, focusing on its potential use in chaos-based communication systems and the control of its Power Spectral Density.

Contribution

It provides a numerical analysis of the quadratic map's spectral properties, addressing challenges in theoretical analysis and implications for communication system bandwidth management.

Findings

Spectral properties of the quadratic map are characterized numerically.

Insights into controlling Power Spectral Density for communication applications.

Highlights the importance of spectral analysis in non-linear dynamical systems.

Abstract

This work numerically examines the temporal and spectral properties of a quadratic map. The quadratic map described in this study has quadratic non-linearity, and its theoretical analysis poses a challenge. Additionally, this map can be used for a fixed parameter value in chaos-based communication systems. Therefore, it is important to understand and, if possible, control the Power Spectral Density (PSD) generated by its signals. In practical communication systems, the bandwidth is limited, making it crucial to understand the spectral formatting of the employed signals.