19 5 32 Points Details Scalcet9 9 6 011 In This Example We Used Lotka Volterra Equations To Model Populations Of 1 (41.32 KiB) Viewed 16 times
19 5 32 Points Details Scalcet9 9 6 011 In This Example We Used Lotka Volterra Equations To Model Populations Of 2 (38.41 KiB) Viewed 16 times
19. [-/5.32 Points] DETAILS SCALCET9 9.6.011. In this example, we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows. dR dt = 0.08R(1-0.0002R) - 0.001RW dW = -0.02W + 0.00002RW dt (a) According to these equations, what happens to the rabbit population in the absence of wolves? In the absence of wolves, we would expect the rabbit population to stabilize at (b) Find all the equilibrium solutions. (R, W) = (R, W) - smallest R-value largest R-value (c) The figure below shows the phase trajectory that starts at the point (1,000, 40). WA 70+ 60+ 50- (R, W) = 40- 800 1000 1200 1400 1600 19
Describe what eventually happens to the rabbit and wolf populations. The populations of wolves and rabbits fluctuate around (d) Sketch graphs of the rabbit and wolf populations as functions of time. 1500 1000 500 1900 1000 80 60 20 and 6000 4000 2000 4000 4000+ mi , respectively, and eventually stabilize at those values. 2000 18308 19 5
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