Dadras

Systems / ODEs / Chaotic attractors

A multi-wing chaotic flow with adjustable scroll count.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{x} &= o y z - p x + y \\ \dot{y} &= r y - x z + z \\ \dot{z} &= c x y - e z \end{aligned} \]

Parameters

Symbol	Default	Role
c	2	polynomial-term coefficient (scroll structure)
e	9	polynomial-term coefficient (scroll structure)
o	2.7	polynomial-term coefficient (scroll structure)
p	3	polynomial-term coefficient (scroll structure)
r	1.7	polynomial-term coefficient (dissipation)

State variables: x, y, z

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = - e - p + r$
constant

Equilibria

5 equilibria
0 stable · 5 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.Dadras()
traj = system.run(final_time=100.0, dt=0.01)
ts.plot(traj)

spectrum = ts.analysis.lyapunov_spectrum(system)
ts.analysis.kaplan_yorke_dimension(spectrum)

Reference

Dadras & Momeni (2009), Phys. Lett. A 373, 3637-3642
doi:10.1016/j.physleta.2009.07.088

BibTeX

@misc{dadras,
  title = {Dadras system},
  note = {Dadras & Momeni (2009), Phys. Lett. A 373, 3637-3642},
  doi = {10.1016/j.physleta.2009.07.088}
}