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# Name: Nushrat Esha # I worked on this code with: Xavier Herrera, Fujia Guo # Please do all of your work for this week's lab in this worksheet. If # you wish to create other worksheets for scratch work, you can, but # this is the one that will be graded. You do not need to do anything # to turn in your lab. It will be collected by your TA at the beginning # of (or right before) next week’s lab. # Be sure to clearly label which question you are answering as you go and to # use enough comments that you and the grader can understand your code.

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#1 # X represents the plants because X's differential equations has one outflow which represents the predation rate. # Y represents the herbivores because there is a natural death rate outflow and an outflow from Z, the carnivore, population. # Z represents the carnivores because there is no predation outflow in this differential equation and it contains a natural death rate outflow.

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#2 time series var("X", "Y", "Z") a1 = 5 b1 = 3 a2 = 0.1 b2 = 2 d1 = 0.4 d2 = 0.01 X0 = 1 Y0 = 0.5 Z0 = 8 Xprime = X*(1-X)-((a1*X)/(1+b1*X))*Y Yprime = ((a1*X)/(1+b1*X))*Y - d1*Y - ((a2*Y)/(1+b2*Y))*Z Zprime = ((a2*Y)/(1+b2*Y))*Z - d2*Z t = srange(0,1000,0.1) sol1 = desolve_odeint([Xprime, Yprime, Zprime], ics = [X0, Y0, Z0], times = t, dvars = [X, Y, Z]) timeseries1 = list_plot(list(zip(t, sol1[:, 0])), plotjoined = True, color = "magenta", legend_label = "plants") + list_plot(list(zip(t, sol1[:, 1])), plotjoined = True, color = "blue", legend_label = "herbivores") + list_plot(list(zip(t, sol1[:, 2])), plotjoined = True, color = "green", legend_label = "carnivores", axes_labels = ["Time", "State Variable"]) timeseries1

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#2 trajectory trajectory1 = list_plot(sol1, plotjoined = True, axes_labels = ["plants", "herbivores", "carnivores"]) trajectory1

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#3 time series var("X", "Y", "Z") a1 = 5 b1 = 3 a2 = 0.1 b2 = 2 d1 = 0.4 d2 = 0.01 X0 = 2 Y0 = 2.5 Z0 = 10 Xprime = X*(1-X)-((a1*X)/(1+b1*X))*Y Yprime = ((a1*X)/(1+b1*X))*Y - d1*Y - ((a2*Y)/(1+b2*Y))*Z Zprime = ((a2*Y)/(1+b2*Y))*Z - d2*Z t = srange(0,1000,0.1) sol2 = desolve_odeint([Xprime, Yprime, Zprime], ics = [X0, Y0, Z0], times = t, dvars = [X, Y, Z]) timeseries2 = list_plot(list(zip(t, sol2[:, 0])), plotjoined = True, color = "red", legend_label = "plants2") + list_plot(list(zip(t, sol2[:, 1])), plotjoined = True, color = "purple", legend_label = "herbivores2") + list_plot(list(zip(t, sol2[:, 2])), plotjoined = True, color = "orange", legend_label = "carnivores2", axes_labels = ["Time", "State Variable"]) timeseries1 + timeseries2

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#3 trajectory trajectory2 = list_plot(sol2, plotjoined = True, axes_labels = ["plants", "herbivores", "carnivores"], color = "orange") trajectory1 + trajectory2

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