ON THE HARMONIC BALANCE METHOD FOR CONSTRUCTING A PERIODIC SOLUTION TO A SYSTEM OF AUTONOMOUS INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE AFTEREFFECT

Abstract

The harmonic balance method refers to the type of Galerkin method and is an analytical method that makes it possible to find an approximate solution to a periodic boundary value problem in the form of an analytical expression. This property of the Galerkin method emphasizes its universality for the study of periodic solutions of both differential and integral- differential equations. This article considers the problem of constructing a periodic solution to a system of integral-differential equations with infinite aftereffects. This type of system describes a mathematical model of the interaction of two types of populations with the property of memory in past times.