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Stability Switches in a Logistic Population Model with Mixed Instantaneous and Delayed Density Dependence

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Abstract

The local asymptotic stability and stability switches of the positive equilibrium in a logistic population model with mixed instantaneous and delayed density dependence is analyzed. It is shown that when the delayed dependence is more dominant, either the positive equilibrium becomes unstable for all large delay values, or the stability of equilibrium switches back and force several times as the delay value increases. Compared with the logistic model with the instantaneous term and a delayed term, our finding here is that the incorporation of another delayed term can lead to the occurrence of multiple stability switches.

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Acknowledgments

The authors would like to thank the anonymous reviewer for careful reading and helpful comments. Partially supported by National Natural Science Foundation of China (11261028), Gansu Province National Natural Science Foundation (145RJZA216) and China Scholarship Council (for X.-P. Yan), and NSF Grant DMS-1022648 and DMS-1313243 (for J.-P. Shi).

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, China

    Xiangping Yan

  2. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Junping Shi

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  1. Xiangping Yan
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  2. Junping Shi
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Correspondence to Junping Shi.

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Yan, X., Shi, J. Stability Switches in a Logistic Population Model with Mixed Instantaneous and Delayed Density Dependence. J Dyn Diff Equat 29, 113–130 (2017). https://doi.org/10.1007/s10884-015-9432-3

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  • DOI: https://doi.org/10.1007/s10884-015-9432-3

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