Linear estimate for the number of limit cycles of a perturbed cubic polynomial differential system

作者：Llibre, Jaume^*; Wu, Hao; Yu, Jiang

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 70(1): 419-432.

DOI：10.1016/j.na.2007.12.010

• Limit cycle
• Averaging theory
• Polynomial differential system

Perturbing the cubic polynomial differential systems (x) over dot = -y (a(1)x + a(0)) (b(1)y + b(0)), (y) over dot = x (a(1)x + a(0)) (b(1)y + b(0)) having a center at the origin inside the class of all polynomial differential systems of degree n, we obtain using the averaging theory of second order that at most 17n + 15 limit cycles can bifurcate from the periodic orbits of the center.

• 出版日期2009-1-1
• 单位上海交通大学