The Lorenz system is a system of ordinary differential equations (the Lorenz equations, note it is not Lorentz) first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.
The exerxise 3.29ask us to explore the intermittency route to chaos for in more details.
From a technical standpoint, the Lorenz system is nonlinear three-dimensional and deterministic system. The Lorenz equations have been the subject of hundreds of research articles, and at least one book-length study.
Thanks to Chwn yangyao for his template.