Spatio-temporal delays in a nutrient-plankton model on a finite domain: linear stability and bifurcations

摘要

The issue of how to incorporate time-delays into a mathematical model in which individuals are moving around requires careful consideration. Any time-delay term must also involve a weighted spatial averaging to account for movement of individuals during the time-delay period. Most of the current literature on this subject is on reaction–diffusion equations and concentrates on the simplest case when the spatial domain is infinite. In this paper we consider what changes arise when the domain is finite. Spatial averaging kernels are computed explicitly for the case of a finite, one-dimensional domain. To illustrate the ideas we concentrate on a diffusive nutrient-plankton model. The model is analysed in terms of the local stability of the steady states and bifurcations. The results of some numerical simulations are also presented.