The L**ogistic Map** is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst.

Mathematically, the logistic map is written

where:

is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year

*n*, and hence

*x*0 represents the initial ratio of population to max. population (at year 0)

*r* is a positive number, and represents a combined rate for reproduction and starvation.

For approximate Continuous Behavior set 'R Base' to a small number like 0.125To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1

To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps