No book on scientific computing is complete without revisiting Lorenz attractors; SciPy excels both at computation of solutions and presentation of ideas based upon systems of differential equations, of course, and we will show how and why in this section.
Consider a two-dimensional fluid cell that is heated from underneath and cooled from above, much like what occurs with the Earth's atmosphere. This creates convection that can be modeled by a single partial differential equation, for which a decent approximation has the form of the following system of ordinary differential equations:
The variable x represents the rate of convective overturning. The variables y and z stand for the horizontal and vertical temperature variations, respectively. This system depends on four physical parameters, the descriptions of which are far beyond the scope of this book. The important point is that we may model Earth's atmosphere with these equations, and in that case a good choice for the...
