# Lorenz Equations and Equilibrium

Please see the attached file for the fully formatted problems.

Show that for , the equilibrium (x*, y*, z*) = (0, 0, 0) is globally (nonlinearly) stable for the Lorenz system. That is, any (x(t), y(t), z(t)) would eventually approach (0, 0, 0) as .

Consider the "volume"

(a) Show that, using the Lorenz equations:

(b) Show that is strictly negative unless one reaches (x, y, z) = (0, 0, 0). Thus argue that the point (0, 0, 0) is the final destination of all trajectories (x, y, z) for

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:58 pm ad1c9bdddfhttps://brainmass.com/math/consumer-mathematics/lorenz-equations-equilibrium-19723

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Show that for , the equilibrium (x*, y*, z*) = (0, 0, 0) is globally (nonlinearly) stable for the Lorenz system. That is, any (x(t), y(t), z(t)) would eventually approach (0, 0, 0) as .

Consider the ...

#### Solution Summary

Lorenz Equations and Equilibrium are investigated.