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Robert May's population growth model

Where:

yt

yt+1

r

The X axis represents increasing values of the population growth factor(r)

The Y axis represents the population level (y)

For each value of r, the equation is iterated 100 times, during which time nothing is drawn to the screen (hidden iterations). Following that, the equation is further iterated by a user definable amount. Each of these iterations plots a point vertically at the current population level.

For values of r below 3, the diagram shows a single steady state population. For values of r between 3 and about 3.57 a series of 'period doubling' occurs (ie: the final population alternates between 2 or more values). Values of r above about 3.57 produce chaotic population levels.