An example of a simple model based on atmospheric fluid dynamics is the Lorenz equations developed by the American meteorologist Edward Lorenz, 2. dx = -ox + oy (28.6) dt dy = rx - y - XZ dt (28.7) dz = -bz + xy dt (28.8) Lorenz developed these equations to relate the intensity of atmospheric fluid motion, x. to temperature variations y and z in the horizontal and vertical directions, respectively. As with the predator-prey model, we see that the nonlinearity is localized in simple multiplicative terms (xz and xy). Use numerical methods to obtain solutions for these equations. Plot the results to visualize how the dependent variables change temporally. In addition, plot the dependent variables versus each other to see whether any interesting patterns emerge.

An example of a simple model based on atmospheric fluid dynamics is the Lorenz equations developed by the American meteorologist Edward Lorenz, 2. dx = -ox + oy (28.6) dt dy = rx - y - XZ dt (28.7) dz = -bz + xy dt (28.8) Lorenz developed these equations to relate the intensity of atmospheric fluid motion, x. to temperature variations y and z in the horizontal and vertical directions, respectively. As with the predator-prey model, we see that the nonlinearity is localized in simple multiplicative terms (xz and xy). Use numerical methods to obtain solutions for these equations. Plot the results to visualize how the dependent variables change temporally. In addition, plot the dependent variables versus each other to see whether any interesting patterns emerge.