3. Integrate the following set of ODE's on the computer: dy da dz (-2) -...

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3. Integrate the following set of ODE's on the computer: dy da dz α (ρ-2) - y. o (y-) = xy - Bz dt dt dt -1 and z(0) using the Improved Euler Method. The initial conditions are x(0)= 1, y(0) and the parameters take on the values a = and run it until t 30 10, B8/3 and p 100, implying that you take 100/0.005 28. Use a step size of h 0.005 20, 000 steps. (It's about time we saw what computers can do!). Display your output by plotting z(t) on the y-axis and x(t) on the x-axis. Does the result look familiar? This is the Lorenz attractor that started the study of chaos. See http://mathworld.wolfram.com/LorenzAttractor.html 3. Integrate the following set of ODE's on the computer: dy da dz α (ρ-2) - y. o (y-) = xy - Bz dt dt dt -1 and z(0) using the Improved Euler Method. The initial conditions are x(0)= 1, y(0) and the parameters take on the values a = and run it until t 30 10, B8/3 and p 100, implying that you take 100/0.005 28. Use a step size of h 0.005 20, 000 steps. (It's about time we saw what computers can do!). Display your output by plotting z(t) on the y-axis and x(t) on the x-axis. Does the result look familiar? This is the Lorenz attractor that started the study of chaos. See http://mathworld.wolfram.com/LorenzAttractor.html

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