Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255097 | Chaos, Solitons & Fractals | 2014 | 11 Pages |
Abstract
The pendulum equation x¨=-αx-δxÌ-(1+f0cosÏ1t)sinx+f1sinÏ2t is considered in this paper, where f0,f1 and δ are small real parameters, the ratio of Ï1 and Ï2 is irrational, and frequencies Ï1 and Ï2 satisfy the Diophantine condition. The unperturbed system (f0=f1=δ=0) has several fixed points for different parameter α. We use KAM theory to prove that the perturbed system possesses quasi-periodic solutions in neighborhoods of those fixed points.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Lin Lu, Xuemei Li,