Database Reference
In-Depth Information
F(X), G(X)
F(X), G(X)
F(X), G(X)
R
R
R
Q
Q
Q
c
a
b
Fig. 14.5
F(X), G(X)
F(X), G(X)
R
R
a
b
Q
Q
Fig. 14.6
R
/Q. Equilibria
The left side of equation (14.13) is a straight line F(X) with slope
−
occur where this line intersects with G(X).
S and R increase with increases in Q. At first, there is a single equilibrium, corre-
sponding to the situation shown in Figure 14.5(a). After some time, the line becomes
tangent to the curve, as shown in Figure 14.5(b). With further increases in the slope,
two points that “attract” system behavior emerge (Figure 14.5(c))—these are the
two outer points.
As the slope of R increases even further, another point of tangency is realized,
(Figure 14.6(a)) and from thereon, only one point of intersection (Figure 14.6(b)), a
stable attractor, persists:
The cusp of the spruce budworm dynamics is shown schematically in the R-Q
plane of Figure 14.7. The upper part of the surface corresponds to an outbreak level
while the lower part corresponds to a subsistence level.
The modules to solve for the dynamics of the spruce budworm population are
shown in Figures 14.8 to 14.10.
We drive changes in the model by setting X = TIME. The functions G(X) and
F(X) generated by our STELLA model are shown in Figures 14.11 and 14.12.
