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

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

2008-10-24

arxiv.org/abs/0810.4377v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

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.

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