Article ID Journal Published Year Pages File Type
758988 Communications in Nonlinear Science and Numerical Simulation 2012 13 Pages PDF
Abstract

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.

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Physical Sciences and Engineering Engineering Mechanical Engineering
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