We construct a class of linear Lyapunov functions for Volterra quadratic stochastic operator. Using these functions we improve known results about Ï‰-limit set of trajectories of the Volterra quadratic operators.

In this paper we introduce a notion of F âˆ’ quadratic stochastic operator. For a wide class of such operators we show that each operator of the class has unique fixed point. Also we prove that any trajectory of the F-quadratic stochastic operator converges to the fixed point exponentially fast.

In this paper, we attempt to provide mathematical models of Mendelian and Non-Mendelian inheritances of the bisexual population system having Fisher's 1:1 principle. In our model, we always assume that distributions of the same phenotype of female and male populations are equal. We study the evolution of a Mendelian trait. As an application of aâ€¦ (More)

We consider a class of Volterra cubic stochastic operators. We describe the set of fixed points, the invariant sets and construct several Lyapunov functions to use them in the study of the asymptotical behavior of the given Volterra cubic stochastic operators. A complete description of the set of limit points is given, and we show that such operators haveâ€¦ (More)