l - Volterra Quadratic Stochastic Operators: Lyapunov Functions, Trajectories

Аннотация

We consider l-Volterra quadratic stochastic operators defined on (m − 1)-dimensional simplex, where ` ∈ {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 ω- limit points of trajectories. We describe a set of fixed points of l-Volterra operators.