Demonstration: Lorenz Equation

• The Lorenz equation is a non-linear system of three differential equations: \[x'=\sigma (y-x), y'=\rho x -y -x z, z'=-\beta z + x y.\] The constants are chosen as follows: \[\sigma=10, \rho=28, \beta=8/3.\] This animation illustrates the sensitivity to initial conditions exhibited by solutions to the Lorenz equation: Three solutions (in red, blue, and green, respectively) with nearly identical initial conditions are tracked over time.