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Asymptotic Expansions for the Sequences of the Modified Discrete Delay Logistic Model Type

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Abstract

As a consequence of some general results we find the asymptotic expansions for the recurrence \(x_{n+1}=\frac{x_{n}}{1+\beta x_{n-k}}\), \(\beta >0\). This can be viewed as a modified version of the well-known discrete delay logistic model \(x_{n+1}=\frac{\alpha x_{n}}{1+\beta x_{n-k}}\), \(\alpha \ge 1 \), \(\beta >0\). We mention that in this case appear a real constant associated with this sequence. Moreover, for various other recursive sequences we find their asymptotic expansions.

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Acknowledgements

We would like to express our gratitude to the six reviewers for their very careful reading of the manuscript and their many valuable and constructive comments that have improved the final version of the paper.

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  1. Department of Mathematics, Ovidius University of Constanţa, Bd. Mamaia 124, 900527, Constanţa, Romania

    Dumitru Popa

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Popa, D. Asymptotic Expansions for the Sequences of the Modified Discrete Delay Logistic Model Type. Qual. Theory Dyn. Syst. 22, 117 (2023). https://doi.org/10.1007/s12346-023-00819-7

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