Department of Mathematics, University of Utah, Salt Lake City, UT, USA.
J Biol Dyn. 2008 Oct;2(4):428-48. doi: 10.1080/17513750802360853.
We model a chemostat containing an age-structured predator and its prey using a linear function for the uptake of substrate by the prey and two different functional responses (linear and Monod) for the consumption of prey by the predator. Limit cycles (LCs) caused by the predator's age structure arise at Hopf bifurcations at low values of the chemostat dilution rate for both model cases. In addition, LCs caused by the predator-prey interaction arise for the case with the Monod functional response. At low dilution rates in the Monod case, the age structure causes cycling at lower values of the inflowing resource concentration and conversely prevents cycling at higher values of the inflowing resource concentration. The results shed light on a similar model by Fussmann et al. [G. Fussmann, S. Ellner, K. Shertzer, and N. Hairston, Crossing the Hopf bifurcation in a live predator-prey system, Science 290 (2000), pp. 1358-1360.], which correctly predicted conditions for the onset of cycling in a chemostat containing an age-structured rotifer population feeding on algal prey.
我们使用线性函数来模拟含有年龄结构的捕食者及其猎物的恒化器，同时使用两种不同的功能反应（线性和 Monod）来模拟捕食者对猎物的消耗。对于两种模型情况，在低恒化器稀释率下，由于捕食者的年龄结构引起的Hopf 分支会产生极限环（LCs）。此外，对于具有 Monod 功能反应的情况，由于捕食者-猎物相互作用会产生 LCs。在 Monod 情况下的低稀释率下，年龄结构导致在较低的流入资源浓度下发生循环，相反，在较高的流入资源浓度下会阻止循环。这些结果为 Fussmann 等人的类似模型提供了一些启示[G. Fussmann, S. Ellner, K. Shertzer 和 N. Hairston, Crossing the Hopf bifurcation in a live predator-prey system, Science 290 (2000), pp. 1358-1360.]，该模型正确预测了含有年龄结构的轮虫种群以藻类为食的恒化器中循环开始的条件。
