In a remote island in the Pacific there is just one population of butterflies, the plants the butterflies eat, and no other living organisms. Year after year, the weather never changes. Each year, all the butterflies die after laying eggs and the eggs hatch the next year. The "birth rate" defines the number of butterfly eggs that become butterflies.
Because the plant supply is limited, if 1000 butterfly eggs become butterflies, none of the butterflies live long enough to lay eggs. This fact is modeled by the the simplest type of non-linear equation, a quadratic equation:
butterfliesn+1= birthrate*butterfliesn*(1-butterfliesn/1000)
What do you think will happen as you increase the birthrate?
Was your intuition correct?