Behavior of trajectories of a quadratic operator (Q6059317)

This paper mainly considers a two-parametric quadratic stochastic operator which maps a 3-dimensional simplex to itself. First, a set of limit points of trajectories are found. It includes a unique fixed point and all the 2-periodic points. Also, these points are nonhyperbolic. Lastly, the authors prove that when an initial point is taken from the 3-dimensional simplex, the trajectory of this point will converge to a unique 2-periodic orbit of the operator.