Dadras¶

Systems / ODEs / Chaotic attractors

A multi-wing chaotic flow with adjustable scroll count.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{y_{0}} &= o y_{1} y_{2} - p y_{0} + y_{1} \\ \dot{y_{1}} &= r y_{1} - y_{0} y_{2} + y_{2} \\ \dot{y_{2}} &= c y_{0} y_{1} - e y_{2} \end{aligned} \]

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)

Properties¶

Lyapunov spectrum

$+0.4426,\; +0.01993,\; -10.76$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.043$

Divergence ∇·f

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

Equilibria

5 equilibria
0 stable · 5 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Dadras & Momeni (2009), Phys. Lett. A 373, 3637-3642

BibTeX

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