Ergodicity can be demonstrated by comparing the spatial distribution of a single long trajectory with that of a large ensemble of initial conditions. As the time scales increase, the two distributions visually converge to become identical.
Conditions: Applies to the Lorenz equations within a specific parameter range where ergodicity can be proven analytically.; The phase space is projected onto the x and z axes.; An ensemble of approximately 500 million points is used.
Ergodicity can be demonstrated by comparing the spatial distribution of a single long trajectory with that of a large ensemble of initial conditions. As the time scales increase, the two distributions visually converge to become identical.
Conditions: Applies to the Lorenz equations within a specific parameter range where ergodicity can be proven analytically.; The phase space is projected onto the x and z axes.; An ensemble of approximately 500 million points is used.