Rich Dynamics of Discrete Time-Delayed Moran-Ricker Model

The time-delayed Moran-Ricker population model is investigated in this paper with an aim to identify some of its unknown features. In this model, the decline of the essential resources arising from the previous generation emerges as a delay in the density dependency of the population. The random fluctuations in population size may cause the model’s dynamics to change. In this study, we aim to scrutinize the model thoroughly and reveal more properties of the model. A discussion about the fixed points and their stability is presented in a brief way. By studying the normal form of the model through the reduction of the model to the associated center manifold, we show that the model will experience flip (period-doubling), Neimark–Sacker, strong resonances, and period-doubling-Neimark Sacker bifurcations. The bifurcation conditions are extracted with their critical coefficients. Numerical bifurcation analysis confirms the validity of theoretical findings.