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Please complete with Python
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answerhappygod
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Please complete with Python
Please complete with Python
Exercise 4.2: The Lorenz equations One of the most celebrated sets of differential equations in physics is the Lorenz equations: dz dx dt o(y-x), dy dt = rx - y - xz, xy - bz, dt where σ, r, and b are constants. (The names o, r, and b are odd, but traditional they are always used in these equations for historical reasons.) These equations were first studied by Edward Lorenz in 1963, who derived them from a simplified model of weather patterns. The reason for their fame is that they were one of the first incontrovertible examples of deterministic chaos, the occurrence of apparently random motion even though there is no randomness built into the equations. = a) Write a program to solve the Lorenz equations for the case o = 10, r = 28, and b 333 in the range from t = 0 to t = 50 with initial conditions (x, y, z) = (0,1,0). Have your program make a plot of y as a function of time. Note the unpredictable nature of the motion. b) Modify your program to produce a plot of z against x. You should see a picture of the famous "strange attractor" of the Lorenz equations, a lop-sided butterfly-shaped plot that never repeats itself. =
Exercise 4.2: The Lorenz equations One of the most celebrated sets of differential equations in physics is the Lorenz equations: dz dx dt o(y-x), dy dt = rx - y - xz, xy - bz, dt where σ, r, and b are constants. (The names o, r, and b are odd, but traditional they are always used in these equations for historical reasons.) These equations were first studied by Edward Lorenz in 1963, who derived them from a simplified model of weather patterns. The reason for their fame is that they were one of the first incontrovertible examples of deterministic chaos, the occurrence of apparently random motion even though there is no randomness built into the equations. = a) Write a program to solve the Lorenz equations for the case o = 10, r = 28, and b 333 in the range from t = 0 to t = 50 with initial conditions (x, y, z) = (0,1,0). Have your program make a plot of y as a function of time. Note the unpredictable nature of the motion. b) Modify your program to produce a plot of z against x. You should see a picture of the famous "strange attractor" of the Lorenz equations, a lop-sided butterfly-shaped plot that never repeats itself. =