Authors estimated the world economic system stability, using a discrete dynamic model (DDM). DDM allows to describe the state of the world economy (whether it is stable, potentially stable or unstable) at different time intervals by means of a generalized image, a "pictogram". These pictograms are radii of convergence (Julia sets) of DDM approximating polynomials. We used this methodology to analyze the state of the world economic system in the interval from 1963 to 2013. In order to determine the type of stability of the world economy in each year during this period, we solved the following interrelated tasks: determined the coefficients of the approximating polynomials, corresponding to different years; found basins of attraction of these polynomials for different values of the coefficients; determined the patterns of convergence of the basins of attraction thus found; built the Julia sets (the radii of convergence) corresponding to them. The obtained results confirm the conclusion that the development of the world economy is largely unstable. But the stability of the world economic system has increased over the period under review (1963-2013). Moreover, the last world economic crisis was not accompanied by a loss of stability. Based on the obtained results, we conclude that the potential stability of the development of the world economic system and economic crises are not unambiguously related concepts. It is necessary to distinguish between the situations of stable development of the economy and the crisis in the economy.