Mathematica 9 is now available

Wolfram Library Archive


Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings
Title

Limit cycles and integrability in a class of system with a high-order critical point
Author

Li Feng
Journal / Anthology

Nonlinear Dynamics
Year: 2013
Volume: 73
Page range: 665670
Description

In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system Mathematica, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved.
Subjects

*Mathematics
*Mathematics > Calculus and Analysis > Dynamical Systems
Keywords

High-order critical point Nilpotent, critical point Center Focus Bifurcation of limit, cycle