Limit cycles of generalized Lienard polynomial differential systems via averaging theory

作者：Garcia Belen; Llibre Jaume; Perez del Rio Jesus S

来源：Chaos Solitons & Fractals, 2014, 62-63: 1-9.

DOI：10.1016/j.chaos.2014.02.008

Using the averaging theory of first and second order we study the maximum number of limit cycles of the polynomial differential systems
x= y, y= -x -epsilon(h(1)(x) + p(1) (x)y + q(1)(x)y(2) + epsilon(2) (h(2)(x) + p(2)(x)y + q(2)(x)y(2)),
which bifurcate from the periodic orbits of the linear center k = y, = -x, where s is a small parameter. If the degrees of the polynomials h(1), h(2), p(1) p(2), q(1) and q(2) are equal to n, then we prove that this maximum number is [n/2] using the averaging theory of first order, where [.] denotes the integer part function; and this maximum number is at most n using the averaging theory of second order.

• 出版日期2014-6