Qualitative Analysis: Answer to Example1
Example: Consider the following predator-prey system
solution curves in the phase plane is as follows:
- Sketch the R(t)- and F(t)-graphs for the solutions with
initial points A, B, and C.
- Find the longterm behavior of the populations over time.
Answer: First, notice that the point A is an equilibrium point
with non-zero coordinates. If we set
we get the following three points: (0,0), (2.5,0), and (1/0.8,1/1.5).
Clearly, we have
- The sketches of the R(t)- and F(t)- graphs for the solutions with
initial points A, B, and C respectively, are given below
- It is clear that all the solutions on the phase-plane tend
to the equilibrium point A when t goes to infinity. Therefore, in
all the cases, we have
[First Order D.E.]
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