Positive periodic solution of a neutral predator-prey system

In this paper, the existence of a positive periodic solution to the following neutral predator-prey system\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left\{ {\begin{array}{*{20}c} {\dot H(t) = rH(t)\left[ {1 - \frac{{a_1 (t)H(t - \tau ) + a_2 \dot H(t - \tau )}}{K}} \right] - a(t)H(t)P(t)} \\ {\dot P(t) = - b(\dot t)P(t) + \beta (t)H(t)P(t)} \\ \end{array} ,} \right.$$ \end{document} is studied, in which r, a2, K and τ are positive constants, and a1 (t), α(t), b(t) and β(t) are positive continuous functions of period ω.