>[!abstract] >The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist 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. > >In 1963, Edward Lorenz developed a simplified mathematical model for atmospheric convection. The model is a system of three ordinary differential equations now known as the Lorenz equations. The equations relate the properties of a two-dimensional fluid layer uniformly warmed from below and cooled from above. In particular, the equations describe the rate of change of three quantities with respect to time (the rate of convection, the horizontal temperature variation, and the vertical temperature variation) ("Lorenz system", 2025). ## Idea compass - **North** (upstream): [[Navier–Stokes equations]] - **East** (different): — - **South** (downstream): — - **West** (similar): — ## References - Lorenz, E. N. (1963, March 1). [[Deterministic nonperiodic flows]]. _Journal of Atmospheric Sciences_, _20_(2), 130-141. https://doi.org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2 - Lorenz system. (2025, April 15). In *Wikipedia*. https://en.wikipedia.org/w/index.php?title=Lorenz%20system&oldid=1282204701