Nonlinear delay differential equations involving population growth

Conditions are given on the function ƒ, such that population χ(t) given by#x003C7;(t) = μχ(t) + ƒ(χ(t − τ)), becomes extinct or remains globally stable. Our theorems are shown to be applicable to the Nicholsonʹs model of blowflies and the population dynamics of baleen whales. In some of these cases, the function ƒ is unimodal rather than monotone.