Application of the averaging principle to the study of the dynamics of the delay logistic equation (Q1991792)

The subject of this paper is the delay logistic equation \[ \frac{du}{dt} = r[1-a u (t-T)], \] where the coefficients \(r\), \(a\), and the delay \(T\) are fast oscillating functions with a frequency \(\omega\gg 1\). The averaging method is applied to this system. The existence of a periodic solution is shown. Additionally, its asymptotical representation and conditions for stability are obtained.