dx/dt = σ (y - x)
dy/dt = -x z + R x - y
dz/dt = x y - B z
parameters: σ = 10, R = 28, B = 8/3 (Lorenz used these values)
The step size of the fourth-order Runge-Kutta method: 0.001
Lyapunov exponents (log with base-e): 0.9050, -0.0001, -14.5715
Lyapunov dimension: 2.0621
The sum of the Lyapunov exponents is theoretically the same as -σ - 1 - B.
Reference
Deterministic nonperiodic flow
Edward Norton Lorenz
Journal of Atmospheric Sciences, 20, 130-141 (1963)
DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Computing the Lyapunov spectrum of a dynamical system from an observed time series
Reggie Brown, Paul Bryant, and Henry Don Isaac Abarbanel
Physical Review A 43, 2787-2806 (1991)
Lyapunov Exponents without Rescaling and Reorthogonalization
Govindan Rangarajan, Salman Habib, and Robert D. Ryne
Physical Review Letters 80, 3747-3750 (1998)
programme
lorenz_lyap.c contains the main function.