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arXiv · 0810.4377

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

U. A. Rozikov·A. Zada
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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 $ω$- limit points of trajectories. We describe a set of fixed points of $\ell$-Volterra operators.

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U. A. Rozikov, A. Zada. 2008-10-24. $\ell$- Volterra Quadratic Stochastic Operators: Lyapunov Functions, Trajectories. https://arxiv.org/abs/0810.4377

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