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In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form(1)ẋ=x(2-a20x2-a11xy-a02y2),ẏ=y(-3+b20x2+b11xy+b02y2),which fulfillment yields the existence in a neighborhood of the origin of a first integral of the form ϕ(x,y)=x3y2+h.o.t., in which case the origin is termed a 2:-3 resonant center. This system was studied in [13], where, due to computational constrains,...
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