On a two lag differential delay equation

Abstract

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 T 2 > T 1 > 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 T 2 / T 1 is large. These may correspond to splitting of major peaks in population density observations.