Stability and monotonicity of Lotka–Volterra type operators

In the present paper,we investigate stability of trajectories ofLotka–Volterra (LV) type operators defined in finite dimensional simplex.We prove that any LV type operator is a surjection of the simplex. It is introduced a newclass of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators

A Generalized Model of Nonlinear Operators of Volterra Type and Lyapunov Functions

В задачах популяционной генетики появляется необходимость изучения асимптотического поведения траекторий нелинейных отображений конечномерного симплекса в себя. Статья посвящена исследованию гомеоморфности таких отображений и изучению поведения траекторий. Гомеоморфизм позволяет описать предысторию эволюции биологической системы.In some problems of population genetics we deal with studying asymptotic behavior of the trajectory of nonlinear mappings of a simplex into itself. The present paper is devoted to investigation of homeomorphisms of such mappings and asymptotic behavior. Such a homeomorphism allows us to determine the pre-history of a biological system