Python Code for Lorenz Plots and Lyapunovs



The Lorenz system is a system of ordinary differential equations which are de fined as :

dx/dt = \sigma (y-x))

dy/dt = x (\rho-z)) -y

dz/dt = xy -\beta z

where \sigma, \rho, and \beta are system parameters. The most commonly used values for them are 10, 28, and 8/3 respectively. At these and nearby parameters, the system displays chaos and revolves around two points or attractors. The equations were first studied by Edward Lorenz, meteorologist working for MIT in 1960. He developed them as part of a model for nonlinear thermal convection, and soon afterward noticed that they display chaos. One particularly notable thing about this system is the relation to the Maxwell-Bloch equations.


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