STABILITY OF A SINGLE-SPECIES POPULATION-MODEL WITH TIME LAG

The stability of equilibrium positions of a single-species population model suggested by Ayala et al. (1973) is studied in the presence of time lag and constant forcing term p. This model is a generalization of the well known logistic model and depends on an additional parameter θS. It is shown that for θ ≥1 the maximum delay for which stability holds decreases as p increases while for 0< θ ≤ ½ it increases. The maximum delay for ½ < θ < 1 is not monotone and has a unique minimum. The conditions that equilibrium position be stable for all time lags are also obtained. © 1979 Taylor & Francis Group, LLC.