PERIODIC 2-PREDATOR, ONE-PREY INTERACTIONS AND THE TIME-SHARING OF A RESOURCE NICHE
PERIODIC 2-PREDATOR, ONE-PREY INTERACTIONS AND THE TIME-SHARING OF A RESOURCE NICHE
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DOI：
10.1137/0144026
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发表时间：
1984-01-01
影响因子：
1.9
通讯作者：
CUSHING, JM
中科院分区：
文献类型：
--
作者：
CUSHING, JM
假设系统参数在时间上是周期性的，则研究了涉及两种竞争性捕食者物种和单一可再生资源被捕食者物种的竞争模型。通过全局分岔技术表明，正周期解的连续体作为选定（平均）参数的函数而存在，并且这些解的稳定性（至少局部接近分岔）取决于分岔的方向。在恒定参数的特殊自治情况下，分岔是垂直的，并且连续谱的谱是离散点。这种自治情况支持竞争排斥原则，因为只有在测量值为零的参数集上，捕食者才能在单一资源猎物上共存（在系统平衡的意义上）。然而，在周期性系数的更一般情况下，如果捕食者参数振荡在某种意义上是异相的，则频谱可以是正长度的间隔，因此这种振荡如何促进稳定共存的可能性。当除捕食者资源消耗率被视为围绕正平均值的小幅度余弦振荡外，所有系统参数均恒定时，对具体情况进行了详细的分析和数值研究。除了说明和证实一般结果外，该示例还清楚地显示了对频谱间隔的影响，从而显示了异相资源消耗率可能对捕食者稳定共存的可能性的影响。
A competition model involving two competing predator species and a single renewable resource prey species is studied under the assumption that the system parameters are periodic in time. It is shown by means of global bifurcation techniques that a continuum of positive periodic solutions exists as a function of a selected (averaged) parameter and that the stability of these solutions (at least locally near bifurcation) depends on the direction of bifurcation. In the special autonomous case of constant parameters the bifurcation is vertical and the spectrum of the continuum is a discrete point. This autonomous case supports the principle of competitive exclusion in that coexistence of the predators on the single resource prey is possible (in the sense that the system equilibrates) only on a parameter set of measure zero. In the more general case of periodic coefficients, however, it is shown that the spectrum can be an interval of positive length provided the predator parameter oscillations are out-of-phase in a certain sense and hence how such oscillations can promote the possibility of stable coexistence. The specific case, when all system parameters are constant except the predator resource consumption rates which are taken to be small amplitude cosine oscillations around a positive mean value, is studied in detail both analytically and numerically. Besides illustrating and corroborating the general results, this example clearly shows the effect on the spectral interval, and hence on the possibility of stable coexistence of the predators, which out-of-phase resource consumption rates can have.