Oscillation and global attractivity in hematopoiesis model with periodic coefficients.
The author considers the following nonlinear delay differential equation \[ p'(t)= {\beta(t) p^m(t- k\omega)\over 1+ p^n(t- k\omega)}- \gamma(t) p(t),\tag{1} \] where \(k\) is a positive integer, \(\beta(t)\) and \(\gamma(t)\) are positive periodic functions of period \(\omega\). The main result for the nondelay case is Theorem 2.1, where the author proves that (1) has a unique positive periodic solution \(\overline p(t)\). He also studies the global attractivity of \(\overline p(t)\). In the delay case, sufficient conditions for the oscillation of all positive solutions to (1) about \(\overline p(t)\) are given, also some sufficient conditions for the global attractivity of \(\overline p(t)\) are established. It should be noted that (1) is a modification of an equation proposed as a model of hematopoiesis. Similar equations are also used as models in population dynamics.
scientific article; zbMATH DE number 1957166