An Analogue Rotated Vector Field of Polynomial System

A class of polynomial system was structured, which depends on a parameter δ. When D monotonous 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.