Discrete Population Growth with Stochastic Effects by Mike Martin

On this page, you can investigate the behavior of the discrete growth model given by

when r takes on random values within δ-units from its central value. More precisely, r is a random variable uniformly distributed in that interval. The user must input the central r-value (denoted by r), the value of δ, the initial population b_{o}, and the number of generations N. The per-capita reproduction rate is not allowed to go below zero. The output is in the form of two graphs. The first graph consists of the discrete points superimposed on a plot of the solution without stochastic effects. The second plot is the same as the first but on a semi-log scale.

Enter in the value of the parameters r, δ, b_{0}, and N, then press the "Plot" button.

r =

δ =

b_{0} =

N =

References:

MathWorld's Exponential Growth Wikipedia's Exponential Growth

Wikipedia's Exponential Growth