Open AccessThe intermittency and extended dimension induced by truncation error
Author(s) -
Sheng Li-Yuan,
Jia Wei-Yao,
WU Shu-ci,
Xia Guo-Rong
Publication year - 2007
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.56.3753
Subject(s) - intermittency , truncation (statistics) , fixed point , focus (optics) , truncation error , dimension (graph theory) , phase (matter) , physics , statistical physics , mathematical analysis , sequence (biology) , point (geometry) , simple (philosophy) , mathematics , statistics , mechanics , geometry , quantum mechanics , combinatorics , optics , turbulence , philosophy , epistemology , biology , genetics
We further studied the cross-focus system and found direct experimental evidence for the truncation error induced intermittency. The experiment demonstrated that, the numerical solution of the cross-focus system shows features of on-off intermittency, while the analytical solution of the cross-focus system is only a simple limited sequence, and the shadowability controls the system evolution. The accumulation of truncation errors imply the shadowing distances of evolving orbits, and the shadowing distance increases on approaching the fixed point and decreases on leaving the fixed point, and the increment equals the decrement in the cycles statistically. In the vicinity of nonhyperbolic fixed point, there is a threshold value, when the accumulation surpasses this threshold value, a tailure of the shadowability takes place, the system jumps from the attraction phase to the repulsion phase. It is reasonably conjectured that a new extended dimension may occur locally in the vicinity of nonhyperbolic fixed point due to truncation errors.