Fast Detection of Weak Singularities in a Chaotic Signal Using Lorenz System and the Bisection Algorithm

Author:

Song Tiezheng1,Cattani Carlo2

Affiliation:

1. School of Electrical Engineering and Automation, Hefei University of Technology, Anhui Province, Hefei City 230009, China

2. Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Abstract

Signals with weak singularities are important for condition monitoring, fault forecasting, and medicine diagnosis. However, the weak singularity in a signal is usually hidden by strong noise. A novel fast method is proposed for detecting a weak singularity in a noised signal by determining a critical threshold towards chaos for the Lorenz system. First, a rough critical threshold value is calculated by local Lyapunov exponents with a step size 0.1. Second, the exact threshold value is calculated by the bisection algorithm. The advantage of the method will not only reduce the computation costs, but also show the weak singular signal which can be accurately identified from strong noise. When the variance of an external signal method embeds into a Lorenz system, according to the parametric equivalent relation between the Lorenz system and the original system, the critical threshold value of the parameter in a Lorenz system is determined.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Limit Cycles from Perturbed Center on the Invariant Algebraic Surface of Unified Lorenz-Type System;International Journal of Bifurcation and Chaos;2023-11

2. Complex Dynamics in the Unified Lorenz-Type System;International Journal of Bifurcation and Chaos;2014-04

3. Dynamic Analysis of the Nonlinear Chaotic System with Multistochastic Disturbances;Journal of Applied Mathematics;2014

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