Global dynamics of a special class of nonlinear semelparous Leslie matrix models |
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Authors: | Yunshyong Chow |
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Affiliation: | Academia Sinica and National Central University, Taipei and Tao-yuan, Taiwan |
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Abstract: | 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. |
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Keywords: | Semelparous Leslie matrix model Leslie–Gower model Kolmogorov difference equation with cyclic symmetry global asymptotic stability asymptotic behaviour periodical insect |
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