Chaos Lab

Continuous flow · dim 3

Rössler

Otto Rössler's 1976 minimal chaotic ODE: only one nonlinearity (the xz product). Single-scroll attractor; the simplest known continuous-time chaotic system.

Rössler attractor (a = b = 0.2, c = 5.7). Single scroll.

Equations

dx/dt = −y − z
dy/dt = x + a y
dz/dt = b + z (x − c)

At a glance

Parametersa = 0.2, b = 0.2, c = 5.7 (classical)
Chaotic formany parameter values; classical c = 5.7
Lyapunov exponentλ₁ ≈ 0.0714 (classical)
HistoryRössler, 'An equation for continuous chaos', Phys. Lett. A (1976).

Try it

Open the interactive playground at /tools/rossler.

See also

Quick quiz

Test yourself on rossler

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.Rössler's 1976 motivation was:

  2. Q2.Rössler attractor at classical (0.2, 0.2, 5.7) has λ₁ approximately:

  3. Q3.Geometrically the Rössler attractor is:

  4. Q4.How many nonlinear terms does the Rössler system have?

  5. Q5.Rössler attractor's Kaplan-Yorke dimension is approximately:

  6. Q6.Increasing c through 5.7 typically takes Rössler:

  7. Q7.Otto Rössler is a:

  8. Q8.Compared to Lorenz, the Rössler equations are:

0 of 8 answered