# The celebrated Lorentz attractor is described by the differential equations [frac{d x}{d t}=-sigma x+sigma y quad, quad

## Question:

The celebrated Lorentz attractor is described by the differential equations

\[\frac{d x}{d t}=-\sigma x+\sigma y \quad, \quad \frac{d y}{d t}=-x z+\alpha x-y \quad, \quad \frac{d z}{d t}=x y-\beta z,\]

and is used to described chaotic fluid dynamics involving heat flow. It is parameterized by \(\alpha, \beta\), and \(\sigma\).

**(a)** Solve this system of equations numerically and plot, for example, \(x\) vs \(y\) and \(z\) vs \(y\). Determine the onset of chaos by testing super-sensitivity to initial conditions.

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