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

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