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We consider limit cycles of a class of polynomial differential systems of the form ẋ = y, where β and α are positive integers, g 2j and f 2j have degree m and n, respectively, for each j = 1, 2, and ε is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center ẋ = y, ẏ = −x using the averaging theory of first and second order.doi:10.21136/mb.2020.0134-18 fatcat:ldnty7webvdczj7njphckrxlvy