Global dynamics of a special class of nonlinear semelparous Leslie matrix models
Global dynamics of a special class of nonlinear semelparous Leslie matrix models
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DOI：
10.1080/10236198.2020.1777288
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发表时间：
2020-05
影响因子：
1.1
通讯作者：
Yunshyong Chow;R. Kon
中科院分区：
文献类型：
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作者：
Yunshyong Chow;R. Kon
摘要：本文研究了非线性半并行Leslie矩阵模型的动力学问题。首先，证明了一类半双Leslie矩阵模型与一类循环对称的Kolmogorov差分方程系统动态一致。然后，完全确定了后者的一类特殊类的全局动力学。结合这两方面，我们得到了一类具有全局渐近稳定正平衡或全局渐近稳定循环的半重Leslie矩阵模型。结果表明，在周期性昆虫中观察到的周期性行为可以作为一种全局稳定的现象发生。
ABSTRACT This paper considers the dynamics of nonlinear semelparous Leslie matrix models. First, a class of semelparous Leslie matrix models is shown to be dynamically consistent with a certain system of Kolmogorov difference equations with cyclic symmetry. Then, the global dynamics of a special class of the latter is fully determined. Combining together, we obtain a special class of semelparous Leslie matrix models which possesses generically either a globally asymptotically stable positive equilibrium or a globally asymptotically stable cycle. The result shows that the periodic behaviour observed in periodical insects can occur as a globally stable phenomenon.