Lorenz system

The Lorenz system is a three-dimensional set of nonlinear differential equations. For certain parameter values, its trajectories form a bounded, aperiodic attractor and vary sensitively with initial conditions.

Lorenz equations: The equations that describe the time evolution of three variables in the Lorenz system. Their nonlinear terms couple convection, temperature difference, and temperature variation.
Edward Lorenz: An American mathematician and meteorologist who introduced the Lorenz system in 1963. His atmospheric modeling work produced the equations and exposed their sensitive dependence.
Ordinary differential equation: An equation relating a function of one variable to its derivatives. Each Lorenz equation specifies how one system variable changes over time.
Chaos theory: The study of deterministic systems whose long-term behavior is highly sensitive to initial conditions. The Lorenz system became a canonical example of deterministic chaos.
Rössler system: A three-dimensional nonlinear differential equation system that exhibits chaotic attractors. It provides a simpler alternative model for studying continuous-time chaos.
Lorenz attractor: The fractal-shaped set toward which trajectories in the Lorenz system approach for certain parameters. It gives the system’s long-term chaotic trajectories their characteristic butterfly-like geometry.
Rayleigh–Bénard convection: Fluid motion in a layer heated from below and cooled from above. The Lorenz equations approximate convection in a simplified fluid layer.
Nonlinear system: A system whose governing equations do not obey linear superposition. Products of variables make the Lorenz equations nonlinear.
Butterfly effect: The idea that small differences in initial conditions can lead to large differences in later outcomes. Lorenz’s model helped make this sensitivity vivid and influential.
Rabinovich–Fabrikant equations: A three-dimensional nonlinear system that exhibits complex dynamics, including chaos. Its chaotic behavior offers a distinct equation set for comparison with Lorenz dynamics.

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