Limit cycles in a sextic Lyapunov system

作者：Li Hongwei^*

来源：Nonlinear Dynamics, 2013, 72(3): 555-559.

DOI：10.1007/s11071-012-0733-3

• Three-order nilpotent critical point
• Center-focus problem
• Bifurcation of limit cycles
• Quasi-Lyapunov constant

Employing the inverse integral factor method, the first 13 quasi-Lyapunov constants for the three-order nilpotent critical point of a sextic Lyapunov system are deduced with the help of MATHEMATICS. Furthermore, sufficient and necessary center conditions are obtained, and there are 13 small amplitude limit cycles, which could be bifurcated from the three-order nilpotent critical point. Henceforth, we give a lower bound of limit cycles, which could be bifurcated from the three-order nilpotent critical point of sextic Lyapunov systems. At last, an example is given to show that there exists a sextic system, which has 13 limit cycles.

• 出版日期2013-5