@article{(Open Science Index):https://publications.waset.org/pdf/8747, title = {Ten Limit Cycles in a Quintic Lyapunov System}, author = {Li Feng}, country = {}, institution = {}, abstract = {In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles. }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {5}, number = {12}, year = {2011}, pages = {1951 - 1953}, ee = {https://publications.waset.org/pdf/8747}, url = {https://publications.waset.org/vol/60}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 60, 2011}, }