Bounding the number of limit cycles for a polynomial Liénard system by using regular chains

Abstract In this paper, we study the bound of the number of limit cycles by Poincare bifurcation for a Lienard 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.

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