Numerical Simulation of Limit Cycles for Two Differential Polynomial Systems

Bifurcation of limit cycles for two differential polynomial systems is investigated using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the differential polynomial systems. The study reveals that each of the two systems has 8 limit cycles using detection function approach. By using method of numerical simulation, the distributed orderliness of these limit cycles is observed and their nicety places are determined. The study also indicates that each of these limit cycles passes the corresponding nicety point.