UBC Theses and Dissertations
Resource recovery delays in harvested predator-prey models Griesmer, Stephen Joseph
This thesis investigates the effect of resource recovery delays, both continuous and discrete, on the behaviour and population dynamics of harvested predator-prey systems. Three models were tested with respect to local stability, global stability, and state-space trajectories. The method of D-partitions was used to determine local stability properties while simulations were performed to discover global properties. Generally, delays were found to induce multiple transitions between locally stable and unstable equilibria as harvest rates are changed. This phenomenon occurred under the management strategies of constant-effort harvesting and constant-quota stocking and harvesting. In addition, in the predator-prey models with delay, a high conversion efficiency and a high satiation limit for the predators can effect instability; this is not possible without delays. Global investigations confirmed the local results and extended them to the simultaneous harvesting of the predator and prey for constant-quota harvesting and stocking. The simulations also showed bifurcations in limit cycles as the carrying capacity was altered and as the stocking rates were varied. Nutrient-limited phytoplankton cultures in chemostats were analyzed with the mathematical techniques. It is shown that multiple stability transitions with changes in dilution rates are theoretically possible but observed delays are not large enough to produce this behaviour.
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