We could use the equation, |
Pn+1 = (1 + B - D)⋅Pn - C*(Pn - 1)⋅Pn/2. |
but our later calculations will be much simpler if we spend a bit of time now recasting the model. |
Instead of measuring the actual population
number Pn, suppose instead we use the related variable
|
In terms of xn, the population equation becomes |
xn+1 = (1 + B - D + C/2)⋅xn⋅(1 - xn) |
This is still too long, so we give the coefficient (1 + B - D + C/2) the name s. Finally, we have the Logistic Map |
xn+1 = s⋅xn⋅(1 - xn) |
the idealized model of a single-species wth limited resources. Robert May's pioneering study of this model, "Simple mathematical models with very complicated dynamics," is one of the main catalysts for the current interest in chaos. |
Return to the Logistic Map.