Stochastic-dynamic treatment of two deterministic chaotic flows in the phase space

It is reasonable to apply stochastic approach to chaotic deterministic nonlinear dynamical systems. In this note we choose two extremely simple 3-dimensional systems (3) and (4) (we call them 'mother systems') and derive respective stochastic-dynamic analogues-'daughter systems' (9)-(11) and (15)-(17). The latter are unclosed and consist of nine equations for twelve unknown phase variables - mean values (Mi), variances ( Cii ) and covariances( Cij , Cijk ). Some speculations on the arising closure problem are presented. Further study requires numerical integration of the derived systems and analysis, and it is left for a later time. (author)