Neutral delay equations from and for population dynamics

K. P. Hadeler, Arizona State University Tempe, AZ, U.S.A.

E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 11. (2008), pp. 1-18.

Abstract: For a certain class of neutral differential equations it is shown that these equations can serve as population models in the sense that they can be interpreted as special cases or caricatures of the standard Gurtin-MacCamy model for a population structured by age with birth and death rate depending on the total adult population. The delayed logistic equation does not belong to this class but the blowfly equation does. These neutral delay equations can be written as forward systems of an ordinary differential equation and a shift map. There are several quite distinct ways to perform the transformation to a system, either following a method of Hale or following more closely the renewal process. Similarly to the delayed logistic equation, the neutral equation (and the blowfly equation as a special case) exhibit periodic solutions, although only for a restricted range of parameters.

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