Analysis of a class of distributed delay logistic differential equations

In this paper, we consider the illustrative example of generalised logistic equations where the carrying-capacity effect is modelled by a distributed-delay effect (which may be over the infinite past). These distributed delay differential equations, though simple in structure, possess a rich array of solutions. If the delay is sufficiently large a supercritical Hopf bifurcation occurs, which finally disappears asymptotically when the delay becomes distributed infinitely. This mirrors the situation when there is just a point delay. Similar models with two or more state variables occur in pasture mixtures.