Math 145, Winter 99: Chaos Theory


Lab #1, Week 02: Population dynamics, an exemplary 1D flow

In Week 2, we continue with 1D flows in the Stella environment, and introduce the Maple environment with the same example:

1D population dynamics

The dynamical system in this example is the logistic equation:
x' = rx(1-x)
where:
  • x denotes the population density, positive
  • r is a rate constant, positive

Software

Stella model
Stella models may be downloaded and run in Stella 5.1.1.
Explore a bunch of trajectories using the Sensi Specs menu item.
Maple worksheet
Maple script may be downloaded and then openned in MapleVr5.
Create a flock of initial conditions by editing thet "ini" list.
Maple script (text)

Recommended experiments

  • Change the parameters in the model, and determine the effects on the trajectory plot.

References


Revised 12 Feb 1999 by Ralph