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Dynamics and Bifurcations of a Discrete-Time Moran-Ricker Model with a Time Delay

Author

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  • Bo Li

    (School of Finance, Anhui University of Finance & Economics, Bengbu 233030, China)

  • Zimeng Yuan

    (School of Finance, Anhui University of Finance & Economics, Bengbu 233030, China)

  • Zohreh Eskandari

    (Department of Mathematics, Faculty of Science, Fasa University, Fasa 7461686131, Iran)

Abstract

This study investigates the dynamics of limited homogeneous populations based on the Moran-Ricker model with time delay. The delay in density dependence caused the preceding generation to consume fewer resources, leading to a decrease in the required resources. Multimodality is evident in the model. Some insect species can be described by the Moran–Ricker model with a time delay. Bifurcations associated with flipping, doubling, and Neimark–Sacker for codimension-one (codim-1) model can be analyzed using bifurcation theory and the normal form method. We also investigate codimension-two (codim-2) bifurcations corresponding to 1:2, 1:3, and 1:4 resonances. In addition to demonstrating the accuracy of theoretical results, numerical simulations are obtained using bifurcation diagrams and phase portraits.

Suggested Citation

  • Bo Li & Zimeng Yuan & Zohreh Eskandari, 2023. "Dynamics and Bifurcations of a Discrete-Time Moran-Ricker Model with a Time Delay," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2446-:d:1155531
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    References listed on IDEAS

    as
    1. Neverova, G.P. & Yarovenko, I.P. & Frisman, E.Ya., 2016. "Dynamics of populations with delayed density dependent birth rate regulation," Ecological Modelling, Elsevier, vol. 340(C), pages 64-73.
    2. Nedorezov, Lev V. & Sadykova, Dinara L., 2008. "Green oak leaf roller moth dynamics: An application of discrete time mathematical models," Ecological Modelling, Elsevier, vol. 212(1), pages 162-170.
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    2. Neverova, G.P. & Yarovenko, I.P. & Frisman, E.Ya., 2016. "Dynamics of populations with delayed density dependent birth rate regulation," Ecological Modelling, Elsevier, vol. 340(C), pages 64-73.

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