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Bifurcation of limit cycles at a nilpotent critical point in a septic Lyapunov system
Yusen Wu,Ming Zhang
Keywords:Third-order nilpotent critical point; Center-focus problem; Bifurcation of limit cycles; Quasi-Lyapunov constant
Abstract:
      In this paper, we investigate local behavior including center conditions and bifurcation of limit cycles of an isolated nilpotent critical point for a class of septic polynomial differential systems. With the help of computer algebra system-MATHEMATICA 12.0, the first 15 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The result that there exist 16 small amplitude limit cycles created from the third-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of third-order nilpotent critical point for septic Lyapunov systems.