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

U. A. Rozikov; A. Zada

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

Dynamical Systems 2008-10-27 v1 Functional Analysis

Authors: U. A. Rozikov , A. Zada

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.

Keywords

volterra equations operator theory and elliptic operators operator theory

Cite

@article{arxiv.0810.4377,
  title  = {$\ell$- Volterra Quadratic Stochastic Operators: Lyapunov Functions, Trajectories},
  author = {U. A. Rozikov and A. Zada},
  journal= {arXiv preprint arXiv:0810.4377},
  year   = {2008}
}

Comments

11 pages

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