  Brane-like vertex operators, defining backgrounds with the ghost-matter
mixing in NSR superstring theory, play an important role in a world-sheet
formulation of D-branes and M theory, being creation operators for extended
objects in the second quantized formalism. In this paper we show that dilaton's
beta function in ghost-matter mixing backgrounds becomes stochastic. The
renormalization group (RG) equations in ghost-matter mixing backgrounds lead to
non-Markovian Fokker-Planck equations which solutions describe superstrings in
curved space-times with brane-like metrics.We show that Feigenbaum universality
constant $\delta=4,669...$ describing transitions from order to chaos in a huge
variety of dynamical systems, appears analytically in these RG equations. We
find that the appearance of this constant is related to the scaling of relative
space-time curvatures at fixed points of the RG flow. In this picture the fixed
points correspond to the period doubling of Feigenbaum iterational schemes.
