Chaotic attractors

5 figures

Sec. 1. Lorenz (3)

The Lorenz system $\dot x=\sigma(y-x),\ \dot y=x(\rho-z)-y,\ \dot z=xy-\beta z$ with $\sigma=10,\ \rho=28,\ \beta=8/3$.

lorenz_fig1 ⤓ download
Fig. 1. 3-D attractor
lorenz_fig2 ⤓ download
Fig. 2. $x$–$z$ projection
lorenz_fig3 ⤓ download
Fig. 3. $x$–$y$ projection

Sec. 2. Rössler (2)

The Rössler system $\dot x=-y-z,\ \dot y=x+ay,\ \dot z=b+z(x-c)$ ($a=b=0.2,\ c=5.7$).

rossler_fig1 ⤓ download
Fig. 4. 3-D attractor
rossler_fig2 ⤓ download
Fig. 5. $x$–$y$ projection