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

© 2015, Texas State University - San Marcos. 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 (Formula presented) when perturbed in the class of all quartic polynomial differential systems. Using the averaging theory of first order we show that at least 8 limit cycles bifurcate from the period annulus of the center. Recently this problem was studied by Peng and Feng [9], where the authors found 3 limit cycles.