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

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.