Bifurcation of Limit Cycles for a Quintic System

Bifurcation of limit cycles for a quintic system is investigated using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the quintic system. The study reveals that the quintic system has 8 limit cycles using detection function approach, and two different distributed orderliness of 8 limit cycles for the quintic system are shown. By using method of numerical simulation, these limit cycles are observed and their nicety places are determined. The study also indicates that each of these limit cycles passes the corresponding nicety point. The results presented here are helpful for further investigating the Hilbert's 16th problem.