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Lorenz-system

The Lorenz system is a system of ordinary differential equations. Edward Lorenz found out that theses equations have chaotic solutions for certain parameter values and initial conditions. The Lorenz attractor is a set of chaotic solutions of the Lorenz system.

Solution

We solved these equations using for these initial conditions.. inital_conditions = [0.5,0.51,0.5] # x_0, y_0, z_0 sigma,r,b = 10, 28, 8/3

Screen Shot 1401-05-17 at 1 55 56 PM

Screen Shot 1401-05-17 at 1 56 06 PM

Effects of r

Screen Shot 1401-05-17 at 1 57 18 PM

Butterfly effect

Because of the shape of the plot, Butterfly effect is associated with The Lorenz attractor.

Screen Shot 1401-05-17 at 2 00 16 PM

Screen Shot 1401-05-17 at 2 00 29 PM

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