Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics

In this paper, we shall consider the nonlinear delay differential equation x′ (t) + αV (t)x(t)xⁿ (t - mω)/θⁿ + xⁿ (t - mω) = λ (t), where m and n are positive integers, and V (t) and λ(t) are positive periodic functions of period ω. In the nondelay case, we shall show that (*) has a unique positive periodic solution x̄(t) and provides sufficient conditions for the global attractivity of x̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about x̄(t) and establish sufficient conditions for the global attractivity of x̄(t).