Limit cycles bifurcanting from the period annulus of a uniform isochronous center in a quartic polynomial differential system

We study the number of limit cycles that bifurcate from the periodic solutions surrounding a uniform isochronous center located at the origin of the quartic polynomial differential system =-y xy(x^2 y^2), =x y^2(x^2 y^2), when it is perturbed inside the class of all quartic polynomial differential systems. Using the averaging theory of first order we show that at least 8 limit cycles can bifurcate from the period annulus of the considered center. Recently this problem was studied in Electron. J. Differ. Equ. 95 (2014), 1--14 where the authors only found 3 limit cycles.