Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Oscillations and global attractivity in a discrete delay logistic model

Authors: S. A. Kuruklis and G. Ladas
Journal: Quart. Appl. Math. 50 (1992), 227-233
MSC: Primary 92D25; Secondary 34K15, 92B05
DOI: https://doi.org/10.1090/qam/1162273
MathSciNet review: MR1162273
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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the discrete delay logistic model

$\displaystyle {N_{t + 1}} = \frac{{\alpha {N_t}}}{{1 + \beta {N_{t - k}}}}, \qquad \left( 1 \right)$

where $ \alpha \in \left( {1, \infty } \right), \beta \in \left( {0, \infty } \right)$, and $ k \in \mathbb{N} = \left\{{0, 1, 2,...} \right\}$. We obtain conditions for the oscillation and asymptotic stability of all positive solutions of Eq. (1) about its positive equilibrium $ \left( {\alpha - 1} \right)/\beta $. We prove that all positive solutions of Eq. (1) are bounded and that for $ k = 0$ and $ k = 1$ the positive equilibrium $ \left( {\alpha - 1} \right)/\beta $ is a global attractor.

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DOI: https://doi.org/10.1090/qam/1162273
Article copyright: © Copyright 1992 American Mathematical Society

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