Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Global stability in a nonautonomous genotype selection model

Author: Chuanxi Qian
Journal: Quart. Appl. Math. 61 (2003), 265-277
MSC: Primary 39A11; Secondary 92D10, 92D25
DOI: https://doi.org/10.1090/qam/1976369
MathSciNet review: MR1976369
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Abstract: Consider the nonautonomous difference equation

$\displaystyle y_{n + 1} = \frac{ y_n \exp \left( \beta_n \left( 1 - \sum\nolimi... ...^k \alpha_i y_{n - i} \right) \right)}, n = 0, 1,..., \qquad \left( 0.1 \right)$

where $ k$ is a nonnegative integer, $ \alpha_0, \alpha_1, \dots, \alpha_{k - 1}$ are nonnegative constants, $ \alpha_k$ is a positive constant and $ \left\{ \beta_n \right\}$ is a nonnegative sequence, which is used as a genotype selection model. In this paper, we first establish some criteria for the positive equilibrium of Eq. (0.1) to be globally asymptotically stable. Then some special cases of Eq. (0.1) are investigated further and more global stability results are obtained. Our results also extend and improve some known results in the literature.

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DOI: https://doi.org/10.1090/qam/1976369
Article copyright: © Copyright 2003 American Mathematical Society

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