Consider a simple formula for population growth where gypsy moths lay eggs at the end of the year 1 and the following spring (year 2) twice as many individuals hatch compared to the previous year:
Formally, this can be written as a linear equation:
Verhulst added a correction factor (i.e., carrying capacity):
Note, that due to this additional term, a factor is multiplied by itself - producing feedback and non-linearity. Here, growth now depends non-linearly in what came before.
Not all birthrates are the same, consider how this formula behaves when we vary the birthrate from 0.9 to 4.0