Rossler¶

Systems / ODEs / Chaotic attractors

A single-folded-band attractor built from the minimal nonlinearity — one quadratic term — yet fully chaotic.

continuous · ODE3 dimensionschaoticdissipative

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Definition¶

\[ \begin{aligned} \dot{x} &= - y - z \\ \dot{y} &= a y + x \\ \dot{z} &= b - c z + x z \end{aligned} \]

Parameters¶

Symbol	Default	Role
`a`	`0.2`	feedback strength
`b`	`0.2`	shift
`c`	`5.7`	fold control

State variables: x, y, z

Properties¶

Lyapunov spectrum

$+0.0714,\; 0,\; -5.39$
Sprott (2003), Chaos and Time-Series Analysis

Kaplan–Yorke dimension

$D_{KY} = 2.013$

Divergence ∇·f

$\nabla\!\cdot f = a - c + x$
state-dependent

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

sys = ts.systems.Rossler()
traj = sys.integrate(final_time=100.0, dt=0.01)

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Reference¶

Rössler (1976), Phys. Lett. A 57, 397-398

BibTeX

@misc{rossler,
  title = {Rossler system},
  note = {Rössler (1976), Phys. Lett. A 57, 397-398}
}