Suppose the model of Exercise 20 is replaced by the equations dx dt

− 0.4xs1 2 0.000005xd 2 0.002xy dy dt

− 20.2y 1 0.000008xy

(a) According to these equations, what happens to the insect population in the absence of birds?

(b) Find the equilibrium solutions and explain their significance.

(c) The figure shows the phase trajectory that starts with 100 birds and 40,000 insects. Describe what eventually happens to the bird and insect populations.

(d) Sketch graphs of the bird and insect populations as functions of time.

Transcribed Image Text:

260 y 240 220 200 180 160 140- 120 100 15000 25000 35000 45000 x