$\ell$- Volterra Quadratic Stochastic Operators: Lyapunov Functions, Trajectories

Abstract

We consider $\ell$-Volterra quadratic stochastic operators defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. Under some conditions on coefficients of such operators we describe Lyapunov functions and apply them to obtain upper estimates for the set of $\omega$- limit points of trajectories. We describe a set of fixed points of $\ell$-Volterra operators.