The Mackey-Glass model of respiratory dynamics: review and new results (Q448510)

This article reviews some known properties of the celebrated Mackey-Glass model of respiratory dynamics and presents some new results for models of a more general type such as equations with time-dependent parameters, multiple delays and distributed delays. The problems explored here involve existence, positivity and permanence of solutions, oscillation, and global asymptotic stability. Some general approaches to deal with nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies by listing six open problems and topics for further research.