Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m

On the number of limit cycles of a quartic polynomial system

“…The problem is still open up to now. However, many results have been obtained for some systems of lower degrees such as quadratic, cubic and quartic polynomial systems, see [3,4,1,2,6,8,9,7,5,10]. Benterki and Llibre [1] investigated a quartic polynomial differential system of the formẋ…”