Abstract
In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers ẋ=−y,ẏ=x;ẋ=−y(1−(x2+y2)2),ẏ=x(1−(x2+y2)2); when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders.
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