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

Bo Li, Zimeng Yuan and Zohreh Eskandari ()
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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

Mathematics, 2023, vol. 11, issue 11, 1-14

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.

Keywords: bifurcation; numerical normal form; critical normal form coefficient; Neimark–Sacker; period doubling; strong resonance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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