There are different models that describe behavior of the world economic system. In this work, we use Discrete Dynamic Model (DDM) in order to assess the world economic system stability (sensitivity of its growth to alteration of its parameters). DDM represents an expansion of a function, describing the dependence of the rate of GDP change in the current year on the rate of GDP change in the previous year, in a Taylor series. Its formal expansion up to the polynomial of degree 3 helps to describe qualitatively certain subtle effects of the world GDP dynamics. Coefficients of expansion of the approximating polynomial were determined by the method of least squares using actual values of the rate of the world GDP change. Analysis of characteristics of the approximating polynomials obtained on different time intervals allowed assessing the world economic system stability. We demonstrated earlier that stable states of the world economic system could be characterized by: (1) an attractive fixed point, (2) periodic points or (3) a strange attractor. DDM allows performing a deeper assessment of the world economic system sensitivity to a change in key macro-economic parameters that influence the coefficients of the DDM approximating polynomials. Mandelbrot sets were constructed for that purpose. Their use allowed receiving a more precise assessment of the world economic system stability in different years.