The work considers quadratic operators defined on and The concept of a quadratic stochastic operator was first given in the work of S. N. Bernstein [2], heredity. Quadratic operators as an object of study appeared at the turn of the thirties in the works of Ulam [43], where the problem was posed of studying the behavior of trajectories of quadratic operators. The impossibility of creating sufficiently developed analytical methods due to complex and cumbersome recurrences when studying trajectories and the need to carry out a very large number of calculations when studying specific quadratic operators did not stimulate interest in this problem. The creation of computers in the forties revived interest in the problem of studying the behavior of trajectories of quadratic operators. Ulam and his co-workers [55] carried out computer calculations for a sufficiently large number of quadratic operators.