Toth Damon, Kot Mark
Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195-2420, USA.
Math Biosci. 2006 Jul;202(1):194-217. doi: 10.1016/j.mbs.2006.03.008. Epub 2006 Apr 19.
We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location in parameter space of the Hopf bifurcations for special cases of our model. The onset of cycling is largely independent of both the form of the resource uptake function and the shape of the maternity function.
我们通过将古尔廷 - 麦卡米 [《数学生物科学》43 (1979) 199] 方法与标准恒化器模型相结合，对以非生物资源为食的年龄结构种群进行建模。即使对于原始古尔廷 - 麦卡米模型没有振荡解的简单生育函数，在恒化器稀释率较低时，霍普夫分岔也会产生极限环。我们找到了模型特殊情况下霍普夫分岔在参数空间中的精确位置。循环的开始在很大程度上与资源摄取函数的形式和生育函数的形状无关。
