Population dynamics: an interactive phase diagram

A phase diagram of population dynamics, prepared at the request of students who needed to understand the diagrams presented in "Consequential classes of resources: Subtle global bifurcation with dramatic ecological consequences in a simple population model", John Vandermeer and Aaron King, [i]Journal of Theoretical Biology[/i] 263 (2010) 237–241. Time-derivatives are as given in Eq 5 of the article. They were integrated via a second-order Runga-Kutta technique to obtain trajectories of the C vs. R point. The blue slope field is for dC/dR (=[dC/dt)/(dR/dt)]), and the zero-growth isoclines are per Equation 6 of the article. Move the "Initial Condition" point and vary the parameters to understand the importance of isoclines and the nature of their points of intersection.

 

JimSmithInChiapas

 
Resource Type
Activity
Tags
diagram  differentialequations  dynamics  isocline  phase  population  vectorfield 
Target Group (Age)
19+
Language
English (United States)
 
 
GeoGebra version
4.2
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7699
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