Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities

作者：Benterki Rebiha; Llibre Jaume^*

来源：Journal of Mathematical Analysis and Applications, 2013, 407(1): 16-22.

DOI：10.1016/j.jmaa.2013.04.076

• Limit cycle
• Periodic orbit
• Center
• Reversible center
• Averaging method

In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers %26lt;br%26gt;(x) over dot = -y, (y) over dot = x; %26lt;br%26gt;(x) over dot = -y(1 - (x(2) + y(2))(2)), (y) over dot = x(1 - (x(2) + y(2))(2)); %26lt;br%26gt;when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders.

• 出版日期2013-11-1