Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896449 | Chaos, Solitons & Fractals | 2008 | 7 Pages |
Abstract
In this paper, a three dimensional autonomous system which is similar to the Lorenz system is considered. By choosing an appropriate bifurcation parameter, we prove that a Hopf bifurcation occurs in this system when the bifurcation parameter exceeds a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is presented by applying the normal form theory. Finally, an example is given and numerical simulations are performed to illustrate the obtained results.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Xiaobing Zhou, Yue Wu, Yi Li, Zhengxi Wei,