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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On $(s,t)$-Volterra Quadratic Stochastic Operators of a Bisexual Population

Journal of Applied Nonlinear Dynamics 9(4) (2020) 575--588 | DOI:10.5890/JAND.2020.12.005

U.U.Jamilov , M. Ladra

V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 81, Mirzo Ulugbek str., 100170, Tashkent, Uzbekistan Departamento of Matem'aticas & Instituto of Matem'aticas, University of Santiago de Compostela, Spain

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Abstract

The authors introduce the concept of $(s,t)$-Volterra stochastic quadratic operator in a bisexual population, where each individual belongs either to the male sex group or female sex group. Under some conditions affecting the coefficients of these operators, several Lyapunov functions have been constructed so that the upper bounds for the set of limiting points of the trajectories could be obtained. This study depicts that the set of $(s,t)$-Volterra stochastic quadratic operators is a convex compact set and the extreme points of this set are found. Furthermore, $(s,t)$-Volterra stochastic quadratic operators of the aforementioned population, which have periodic trajectories, are constructed.

Acknowledgments

We thank the referees for the helpful comments and suggestions that contributed to improving this paper. The authors thank Prof. U. A. Rozikov for useful discussions.

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