The boundary of small signal stability region（SSSR） is consisted of three types of local bifurcations of power system modeled by differential-algebraic equations.This paper focuses on the SSSR composed of Hopf bifurcation points.It is found that the boundaries of SSSR are not continuous smoothly and its shape can be changed roughly when the structural stability of system on the boundary is broken.The study shows that the change of characteristics of boundary of SSSR is related with degenerate Hopf bifurcation closely.The degenerate Hopf bifurcation leads to the appearance of two SSSR in 2-dimension parameter space，then attraction and coupling of the two regions result in the sudden changes of boundaries of SSSR.At last it illustrates the SSSR and its connectivity in 3-dimension space.The article shows that the research on the complicated dynamics of nonlinear system is the essential approach to reveal the topological characteristics of SSSR of power system.