In Problems 11 and 12, we consider the effect of modifying the equation for the prey
Consider the system
Where
a) Find all critical points of the given system. How does their location change as
b) Determine the nature and stability characteristics of each critical point.
c) Show that there is a value of
d) Describe the effect on the two population as
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Differential Equations: An Introduction to Modern Methods and Applications
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- Problem 1: In the Lotka-Volterra predator-prey model, the number of foxes and rabbits in a park depend on each other. When there are many rabbits, the population of foxes increases but when there are many foxes, the population of rabbits decreases. The following equation provides the Lotka-Volterra model for the number of foxes, F, and the number of rabbits, R, in Eagle Park. 21.4 = -0.002R+0.4 ln(R) – 0.01F + 4 ln(F). A graph showing the curve given by this equation is given below. dF (a) Find a formula for dR Foxes (b) Based on the graph, what do you expect the dF to be when the number of foxes dR value of 500 in the park is at its highest or lowest value? dF and your answer dR 400 (c) Using your formula for to part (b), determine the number of rabbits in the park when the fox population is at its highest or lowest value. 300 200 (d) Using the model and your answer to part (c), 100 determine the maximum and minimum val- ues for the size of the fox population in Eagle Park. You will…arrow_forwardQuestion 3. Solve the following system of equations: log, (x) +log49 (y*) = log,(xy³) = 6 = 12 [a] := 712, y= 7-6 [b] X1 = 2,y1 = 1 and x = = 12, y= -6 X = [e] not in the list [c] no solution [d] X1 = 7,y1 = 49 and x2 = 1,y2 =7arrow_forward
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