Dynamics of a Convex Combination and Superposition of Non-Volterra Quadratic Stochastic Operators

We consider a convex combination of non-Volterra quadratic stochastic operators defined on the two-dimensional simplex depending on a parameter λ and study their trajectory behaviours. We show that for any λ∈[0, 1] and for any initial point the set of limit points of the trajectory is a singleton. We also prove that a superposition of these non-Volterra quadratic stochastic operators is a regular transformation.