Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
758988 | Communications in Nonlinear Science and Numerical Simulation | 2012 | 13 Pages |
In the present paper, for the three-order nilpotent critical point of a cubic Lyapunov system, the center problem and bifurcation of limit cycles are investigated. With the help of computer algebra system-MATHEMATICA, the first 7 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact of there exist 7 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for cubic Lyapunov systems.
► We give center conditions and 7 limit cycles at three-order nilpotent critical point. ► The first 7 quasi-Lyapunov constants are deduced by MATHEMATICA. ► Sufficiency and necessity to be a center are proved. ► We give a lower bound of cyclicity of three-order nilpotent critical point.