Abstract: A class of polynomial system was structured, which depends on a parameter δ. When δmonotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with the δ. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an “analogue rotated vector field” with δ. They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.

Key words: polynomial system, analogue vector field, limit cycle, Poincar? bifurcation