A double logistic competition model A much better (and
only a bit harder) species competition model than Kudzu world can be written
where , are populations of species one and two relative to
their individual carrying capacity (this is an example of scaling, if
, it means that population one is at its carrying capacity in the
absence of species 2...tricky,tricky,tricky). The constants a
and b affect how much the other species affects each species growth
rate.
- Choose a and b to be any numbers less than 1 then sketch a
phase portrait with nullclines and identify the four fixed points
(hint, the graphing calculator on the Macs might be useful here).
Discuss the stability of the different fixed points. Can you get a
stable population with both species?
- Check your answer with Stella, make a quantitative phase
portrait and discuss the global behavior of this system for
different initial conditions.