Analysis of a class of distributed delay logistic differential equations

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Abstract

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. © 2003 Elsevier Science Ltd. All rights reserved.

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Rasmussen, H., Wake, G. C., & Donaldson, J. (2003). Analysis of a class of distributed delay logistic differential equations. Mathematical and Computer Modelling, 38(1–2), 123–132. https://doi.org/10.1016/S0895-7177(03)90010-0

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