Delay effect in models of population growth (Q1773317)

The authors systematize earlier results on the global stability of the model \[ \frac {dx(t)}{dt}+ \mu x(t)= f(x(t-\tau )) \] of population growth and give a basic comparison theorem. The effect of the delay on the asymptotic behavior is studied. The existence of positive solutions is established for large delay when the nonlinearity \(f\) is a unimodal map. The main results can be applied to several population models. Some earlier result are generalized.