The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Table of Contents - Volume 24 - Issue03

Research Article

On a two lag differential delay equation

R. D. Braddocka1 and P. van den Driesschea2

a1 School of Australian Environmental Studies, Griffith University, Nathan, Queensland 4111.

a2 Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada, V8W 2Y2.

Abstract

The non-linear differential difference equation of the form

S0334270000002939_eqnU1

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.

(Received January 16 1981)

(Revised March 10 1982)

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