Non-synchronous oscillations in four-dimensional nonlinear semelparous Leslie matrix models
Non-synchronous oscillations in four-dimensional nonlinear semelparous Leslie matrix models
复制标题
四维非线性连续Leslie矩阵模型中的非同步振荡
DOI：
10.1080/10236198.2017.1365144
复制
发表时间：
2017
影响因子：
1.1
通讯作者：
Ryusuke Kon
中科院分区：
文献类型：
--
作者：
Chow Yunshyong;Kon Ryusuke;Ryusuke Kon;今隆助;今隆助;Ryusuke Kon
在一类半纯Leslie矩阵模型中，如果模型的维为2或3，则正平衡点稳定而非负锥边界上的不变集不稳定，反之亦然。这种动态二分法预计在四维情况下是失败的。我们的研究集中于一个具有特定非线性的半纯Leslie矩阵模型，并严格证明了动态二分法在四维情形下不成立。这一结果是通过证明四维半纯Leslie矩阵模型可以关于非负锥的边界一致持久的，即使存在不稳定的正平衡点。在这种情况下，没有遗漏年龄类，但出现了种群振荡。
In a certain class of semelparous Leslie matrix models, either a positive equilibrium is stable and an invariant set on the boundary of the nonnegative cone is unstable or vice versa generically if the model dimension is two or three. This dynamic dichotomy is expected to be failed in the four-dimensional case. Our study focuses on a semelparous Leslie matrix model with specific nonlinearities and rigorously proves that the dynamic dichotomy does not hold in the four-dimensional case. This result is derived by showing that the four-dimensional semelparous Leslie matrix model can be uniformly persistent with respect to the boundary of the nonnegative cone even if there exists an unstable positive equilibrium. In such a situation, there are no missing age-classes but population oscillation occurs.