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**1. Homework Statement**

1) Determine the qualitative properties of the One-Dimensional maps:

x_n+1 = f(x_n) = x_n * e^(r * (1 - x_n))

This function has been used by ecologists to study a population that is limited at high densities by the effect of epidemics. Although it is more complicated than the map we have been using, its advantage is that the population remains positive no matter what positive value is taken for the initial population.

2) There are no restrictions on the maximum value of r, but if r becomes sufficiently large, x eventually becomes effectively zero. What is the behavior of the time series of this function for r = 1.5, 2, 2.7. Does f(x) have a maximum?

**2. Homework Equations**

x_n+1 = f(x_n) = x_n * e^(r * (1 - x_n))

**3. The Attempt at a Solution**

1) I don't really understand the question.. Are there any websites about this equation that goes into more detail about each part of the equation? Thanks

2) If you increase the parameter r to a higher value, the time series will increase as well. I wouldn't say that f(x) has a maximum, rather a equilibrium value that it reaches.