Maximum number of limit cycles bifurcating from the period annulus of cubic polynomial systems

Abstract

This paper is devoted to the limit cycle bifurcation problem for some cubic polynomial systems, whose unperturbed systems have a period annulus and two invariant lines. Using the first order Melnikov function and Chebyshev criterion, we obtain the maximum number of limit cycles bifurcating from the period annulus. It improves a known result given by Sui and Zhao [Internat. J. Bifur. Chaos Appl. Sci. Engrg. 28 (2018), 1850063].