Periodic solutions to non-autonomous predator-prey systems with multiple and time-dependent delays

In this paper we establish the existence of at least one positive periodic solution for the following non-autonomous predator-prey systems of delay differential equations:\begin{align*} x'(t)&=\alpha(t)x(t-\tau_{11}(t))f(t,x(t-\tau_{12}(t)),y(t-\tau_{13}(t))),\\ y'(t)&=\beta(t)y(t-\tau_{21}(t))g(t,x(t-\tau_{22}(t)),y(t-\tau_{23}(t))). \end{align*} Our approach considers the coefficients and delays as periodic functions. We apply this approach to specific biological problems and derive sufficient conditions guaranteeing the existence of positive periodic solutions for each case of the system. It is noteworthy that, except for the periodicity of the delays, we do not impose any additional conditions on them.