STUDY OF THE OSCILLATION PERIOD IN THE LOTKA-VOLTERRA MODEL

YGANCQ

Abstract

The system of Lotka-Volterra equations is analyzed. The main goal is to obtain a relationship between the period of population fluctuations and the parameters that determine the course of the process in the predator-prey system. An asymptotic dependence is also derived for the oscillation period when the phase curve of the process approaches close to the origin of the coordinates of the phase plane. Therefore, numerous textbooks and monographs are forced to present results obtained by numerical methods, mainly on the evolution of population concentrations of predators and prey, which makes it difficult to understand how certain model parameters affect the process of interaction between populations in the system.

            The work analyzes the system of Lotka-Volterra equations using both analytical and numerical methods. The main interest is in determining the period of oscillations in the Lotka-Volterra system, which was the main purpose of the study in this work. The work obtained simple analytical dependencies that determine the influence of special (certain) combinations of parameters of the predator-prey model on the period of oscillations in the system.  An asymptotic dependence has also been derived for the oscillation period when the phase curve of the process approaches the origin of coordinates of the phase plane.