Volterra quadratic stochastic operators of a two-sex population

  • U. U. Zhamilov
  • U. A. Rozikov

Abstract

We introduce the notion of Volterra quadratic stochastic operators of a bisexual population. The description of the fixed points of Volterra quadratic stochastic operators of a bisexual population is reduced to the description of the fixed points of Volterra-type operators. Several Lyapunov functions are constructed for the Volterra quadratic stochastic operators of a bisexual population. By using these functions, we obtain an upper bound for the ω-limit set of trajectories. It is shown that the set of all Volterra quadratic stochastic operators of a bisexual population is a convex compact set, and the extreme points of this set are found. Volterra quadratic stochastic operators of a bisexual population that have a 2-periodic orbit (trajectory) are constructed.
Published
25.07.2011
How to Cite
ZhamilovU. U., and RozikovU. A. “Volterra Quadratic Stochastic Operators of a Two-Sex Population”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 7, July 2011, pp. 985-98, http://umj.imath.kiev.ua/index.php/umj/article/view/2779.
Section
Research articles