MODELS DESCRIBED BY BISTOCHASTIC QUADRATIC OPERATORS

Abstract:  
The article introduces the concept of a bistochastic quadratic operator acting in 
the  simplex  1 n S  .  Necessary  and  sufficient  conditions  for  bistochasticity  are 
obtained. It is noticed that the set of all bistochastic quadratic operators acting in  1 n
S ,  forms  a  polyhedron.  The  dynamical  and  statistical  (ergodic)  properties  of  the 
trajectories of bistochastic quadratic operators are investigated.