摘要：In this paper, the center conditions and the conditions for bifurcations of limit cycles from a third-order nilpotent critical point in a class of quartic systems are investigated. Taking the system coefficients as parameters, explicit expressions for the first 11 quasi-Lyapunov constants are deduced. As a result, we prove that 11 or 12 small-amplitude limit cycles could be created from the third-order nilpotent critical point by two different perturbations.
关键词：third-order nilpotent critical point ; center-focus problem ; bifurcation of limit cycles ; quasi-Lyapunov constant
