On a Difference Equation with Exponentially Decreasing Nonlinearity

Figure 1

The graph of the function (3.1) demonstrates that, unlike most unimodal functions in population dynamics models, 𝑓(𝑥) decreases for small 𝑥 and increases for large 𝑥, thus having a minimum, not a maximum. Here 𝛼=0.5, 𝑝=0.6, 𝑞=2, 𝑥^∗≈0.438, 𝑥≈0.47>𝑥^∗. The graph incorporates some iterations which converge (monotonically, beginning with the second iteration) to the positive equilibrium.