/DS_Lorenz_Attractor

Numerical solution for the Lorenz System

Primary LanguagePython

DS_Lorenz_Attractor

similar to the Rossler simulation

Method

Simpletic Runge-Kutta of 4 order

Global Conditions

time_step = 0.01

Initial Conditions

x_0 = 1 y_0 = 1 z_0 = 1

for the Lyapunov calculation a $\delta=1e^{-6}$ was add to the original IC.

Results

original Lorenz attractor

x ts

y ts

z ts

Lyapunov Exponent

With a lyapunov exponent of 0.892456 and a Lyapunov time of 1.12050 the system is deterministic and not stochastic.

Taken's Theorem

Taken's theorem used with only the x ts. Here I make a lag of 10 time steps

Takens Theorem with x ts

Takens Theorem with y ts

Takens Theorem with z ts