Magnússon K G
Division of Applied Mathematics and Computer Science, University of Iceland, Reykjavík, Iceland.
Math Biosci. 1999 Jan 1;155(1):61-75. doi: 10.1016/s0025-5564(98)10051-2.
The dynamics of a predator-prey system, where the predator has two stages, a juvenile stage and a mature stage, are modelled by a system of three ordinary differential equations. The mature predators prey on the juvenile predators in addition to the prey. If the mortality rate of juveniles is low and/or the recruitment rate to the mature population is high, then there is a stable equilibrium with all three population sizes positive. On the other hand, if the mortality rate of juveniles is high and/or the recruitment rate to the mature population is low, then the equilibrium will be stable for low levels of cannibalism, but a loss of stability by a Hopf bifurcation will take place as the level of cannibalism increases. Numerical studies indicate that a stable limit cycle appears. Cannibalism can therefore be a destabilizing force in a predator-prey system.
在一个捕食者 - 猎物系统中，捕食者有两个阶段，即幼年阶段和成熟阶段，其动态由一个包含三个常微分方程的系统来建模。除了捕食猎物外，成熟捕食者还会捕食幼年捕食者。如果幼年个体的死亡率较低和/或向成熟种群的补充率较高，那么存在一个所有三种种群规模均为正且稳定的平衡点。另一方面，如果幼年个体的死亡率较高和/或向成熟种群的补充率较低，那么对于低水平的同类相食情况，平衡点将是稳定的，但随着同类相食水平的增加，会通过霍普夫分岔发生稳定性丧失。数值研究表明会出现一个稳定的极限环。因此，同类相食在捕食者 - 猎物系统中可能是一种破坏稳定性的力量。
