Global stability in a periodic delayed predator-prey system (Q876607)

The authors study existence and global attractivity of a positive periodic solution of the periodic delayed predator-prey system \[ \begin{aligned} y_1'(t)&=y_1(t)\left[r_1(t)-a_1(t)y_1(t)+\sum_{i=1}^nb_{1i}(t)y_1(t-\tau_i(t))-\sum_{j=1}^mc_{1j}(t) y_2(t-\rho_{j}(t))\right],\\ y_2'(t)&=y_2(t)\left[r_2(t)-a_2(t)y_2(t)+\sum_{j=1}^mb_{2j}(t)y_2(t-\eta_j(t))+\sum_{i=1}^nc_{2i}(t) y_1(t-\sigma_{i}(t))\right]. \end{aligned}\tag{1} \] By using the method of coincidence degree and a Lyapunov functional, under some assumptions, easily verifiable sufficient conditions are obtained for the existence and global attractivity of a positive periodic solution of (1). Biological interpretations on the main results are also given.