中文摘要：

In this paper,bifurcation of limit cycles for the degenerate equilibrium to a threedimensional system is investigated.Firstly,we use formal series to calculate the focal values at the high-order critical point on center manifold.Then an example is studied,and the existence of 3 limit cycles on the center manifold is proved.In terms of highorder singularities in high-dimensional systems,our results are new.

英文摘要：

In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new.