Bounding the number of limit cycles for a polynomial Liénard system by using regular chains. (March 2017) - Sun, Xianbo; Huang, Wentao
Abstract: In this paper, we study the bound of the number of limit cycles by Poincaré bifurcation for a Liénard system of type ( 4, 3 ) . An automatic algorithm is constructed based on the Chebyshev criteria and the tools of regular chain theory in polynomial algebra. We prove the system can bifurcate at most 6 limit cycles from the periodic annulus by this algorithm and at least 4 limit cycles by asymptotic expansions of the related Melnikov functions.