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On a two lag differential delay equation

Published online by Cambridge University Press:  17 February 2009

R. D. Braddock  and
P. van den Driessche
R. D. Braddock
Affiliation:
School of Australian Environmental Studies, Griffith University, Nathan, Queensland 4111.
P. van den Driessche
Affiliation:
Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada, V8W 2Y2.
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Abstract

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The non-linear differential difference equation of the form

is investigated. This equation, with constant coefficients, is used to model the population level, N, of a single species, and incorporates two constant time lags T2 > T1 > 0; for example, regeneration and reproductive lags. The linear equation is investigated analytically, and some linear stability regions are described. The special case in which the two delay terms are equally important in self damping, B = C, is investigated in detail. Numerical solutions for this case show stable limit cycles, with multiple loops appearing when T2/T1 is large. These may correspond to splitting of major peaks in population density observations.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 3 , January 1983 , pp. 292 - 317
Copyright
Copyright © Australian Mathematical Society 1983

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