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Oscillations in marine and insect populations with delayed density-dependence

par Erneux, Thomas ;Kuang, Yang
Référence Mathematical biosciences and engineering, 23, 5, page (1340-1355)
Publication Publié, 2026-07-01

Article révisé par les pairs

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Résumé :

A scalar delay differential equation with threshold nonlinearity has been formulated to describe the limited growth of sessile marine invertebrates and insect populations when resources are limited. Depending on the settlement and mortality rates of juveniles, sustained oscillations generated by Hopf bifurcations are possible. We construct these time-periodic solutions by using the method of steps and analyze their bifurcation properties. All our analytical results are in agreement with those obtained from numerical simulations of the original delay differential equation. Particular attention is devoted to the Hopf bifurcation points in the limit of a high juvenile settlement rate. In addition, we identify important changes in the periodic waveform when adults exhibit low mortality rates.