| Abstract: |
| Depending upon the underlying assumptions and reason for including delay in a model of population growth, we propose different strategies for deriving discrete models predicting growth of a single population. We then analyze the resulting models. The dynamics of the models that we introduce differ from existing logistic delay difference equations, such as the delayed logistic difference equation that was formulated as a discretization of the Hutchinson model. In all cases, we identify an important critical delay threshold that depends on the length of the delay and other parameters in the model. If the length of the time delay exceeds this threshold, the models predict that the population will go extinct for any non-negative initial conditions. Below this threshold, there is at least one equilibrium at which the population survives. We discuss the number of survival equilibria, their stability, and how their magnitude depend on the length of the delay. |
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