On the behaviour of solutions to discrete time Lotka-Volterra equation
  The time evolution of a class of completely integrable discrete Lotka-Volterra s ystem is shown not unique but have two different ways chosen randomly at every s tep of generation. This uncertainty is consistent with the existence of constant s of motion and disappears in both continuous time and ultra discrete limits. 
Y.Narita, S.Saito, N.Saitoh, K.Yoshida