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.

中文翻译：

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一类特殊非线性次生 Leslie 矩阵模型的全局动力学

摘要 本文考虑了非线性 semelparous Leslie 矩阵模型的动力学。首先，证明了一类semelparous Leslie矩阵模型与具有循环对称性的Kolmogorov差分方程的某个系统动态一致。然后，完全确定后者的一个特殊类的全局动态。结合在一起，我们获得了一类特殊的 semelparous Leslie 矩阵模型，它通常具有全局渐近稳定正平衡或全局渐近稳定循环。结果表明，在周期性昆虫中观察到的周期性行为可以作为全局稳定现象发生。