The following animation allows you to explore the behavior of the logistic model for different values of Rmax. Consecutive points in the plot are joined with line segments to make it easier to see what is happening.
In this project of the textbook we derive the logistic differential equation from the logistic difference equation. To do so we first consider what happens over a time interval of length h, where h<1. We suppose that the change in population size during this interval is proportional to the length of the interval h, just as we did in the ‘Biology Background’ material associated with Page 421 of the textbook.