Oscillation and global attractivity in a periodic delay hematopoiesis model (Q1429358)

The paper deals with the nonlinear delay differential equation \[ p'(t)=\frac{\beta (t)}{1+p^n(t-m\omega)} - \delta (t)p(t), \quad t\geq 0, \tag{1} \] where \(m\geq 0\) and \(n>0\) are integers, and \(\beta (t)\) and \(\delta (t)\) are positive periodic functions with period \(\omega\). The author shows that in the non-delay case (\(m=0\)) equation (1) has a unique positive periodic solution \(\bar p (t)\), and that \(\bar p (t)\) is a global attractor all other positive solutions. In the delay case (\(m>0\)), he derives sufficient conditions for the oscillation of all positive solutions of (1) on \(\bar p (t)\), and gives sufficient conditions for the global attractivity of \(\bar p (t)\). Essential definitions can be found in the paper.