Method for removing interference in chaotic signals based on the Lyapunov exponent

TL;DR

This paper introduces a novel method leveraging Lyapunov exponents and chaos synchronization to effectively remove external interference from chaotic signals, demonstrated on the Lorenz attractor.

Contribution

The paper presents a new interference reduction technique based on chaos properties and Lyapunov exponents, improving signal clarity in chaotic systems.

Findings

Effective removal of external interference demonstrated on Lorenz attractor

Method estimates small deviations using positive Lyapunov exponents

Numerical results confirm the method's effectiveness

Abstract

A new method based on the phenomenon of synchronization and the properties of chaos is proposed to reduce interference in the transferred chaotic signals of synchronized systems. In this paper, the interference is considered as a series of small deviations from the original clean trajectory in the phase space. By means of our special design, these small deviations can be estimated using positive Lyapunov exponents, and removed from interfered chaotic signals. Application is illustrated for the Lorenz attractor, and numerical computing demonstrates that the method is effective in removing typical external interference.