Email this article On the stability of Lotka-Volterra model with a delay
- Authors: Khusanov J.K.1, Kaxxorov A.E.2
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Affiliations:
- Jizzakh Polytechnic Institute
- I. Karimov Tashkent State Technical University
- Issue: Vol 24, No 2 (2022)
- Pages: 175-184
- Section: Mathematics
- Published: 25.05.2022
- URL: https://journals.rcsi.science/2079-6900/article/view/365029
- DOI: https://doi.org/10.15507/2079-6900.24.202202.175-184
- ID: 365029
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Abstract
The paper examines the stability problem of biological, economic and other processes modeled by the Lotka-Volterra equations with delay. The difference between studied equations and the known ones is that the adaptability functions and the coefficients of the relative change of the interacting subjects or objects are non-linear and take into account variable delay in the action of factors affecting the number of subjects or objects. Moreover, these functions admit the existence of equilibrium positions’ set that is finite in a bounded domain. The stability study of three types of equilibrium positions is carried out using direct analysis of perturbed equations and construction of Lyapunov functionals that satisfy conditions of well-known theorems. Corresponding sufficient conditions for asymptotic stability including global stability are derived, as well as instability and attraction conditions of these positions.
About the authors
Jumanazar Kh. Khusanov
Jizzakh Polytechnic Institute
Email: d.khusanov1952@mail.ru
ORCID iD: 0000-0001-9444-9324
Ph.D. (Phys.-Math.), Professor, Jizzakh Polytechnic Institute
Uzbekistan, 4 I. Karimov St., Jizakh 130100, UzbekistanAzizbeck E. Kaxxorov
I. Karimov Tashkent State Technical University
Author for correspondence.
Email: azizqahhorov@gmail.com
ORCID iD: 0000-0001-5723-8640
Graduate Student
Uzbekistan, 2 University St., Tashkent 100095, UzbekistanReferences
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