Open AccessThe research on long range correlation of Lorenz system
Author(s) -
Qiguang Wang,
Zhi Rong,
Zengping Zhang
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.5343
Subject(s) - predictability , detrended fluctuation analysis , scaling , statistical physics , lorenz system , range (aeronautics) , correlation , chaotic , autocorrelation , correlation function (quantum field theory) , initial value problem , noise (video) , physics , mathematics , statistics , mathematical analysis , computer science , spectral density , geometry , materials science , image (mathematics) , artificial intelligence , composite material
This paper takes the typical chaotic system the Lorenz system as the subject. We use the detrended fluctuation analysis method to study the systems long-range correlation for different initial values and parameters. It turns out that the systems long range correlation is related with its initial values phase space position. When the initial value is close to the unstable equilibrium points the systems long rang correlation is strengthened the scaling exponents α are bigger and the predictability of the system is better. When the system is in complete chaotic state its long range correlation becomes weak with the parameters increasing and the scaling exponents α are decrease the predictability of the system becomes weaker. This reveals the relationship between the systems long range correlation and its predictability. We disturbed the system equation with random noise and found that the systems long range correlation decreases with the increase of random noise intensity. This result further signifies out that the Lorenz system's long range correlation is a physical parameter that may serves as an effective predictability criterion.