Dadras Attractor

Attractor Builder (Blender add-on)
Equations:
ẋ = y - a * x + b * y * z
ẏ = c * y - x * z + z
ż = d * x * y - h * z
Parameters:
| a = 3 | b = 2.7 | c = 1.7 | d = 2 | h = 9 |
Simulation settings:
Initial state: x₀ = 0.01, y₀ = 0.01, z₀ = 0.01
Method: DP5
Tolerance: 0.0001
Min step: 0.000001
Max step: 0.1
Steps: 10000
Burn-in: 2000
Scale: 0.2

The Dadras attractor was introduced by Sara Dadras and Hamid Reza Momeni (2009) as a new three-dimensional autonomous chaotic system capable of generating two, three, and four-scroll attractors by varying a single parameter. The system features five real equilibria and rich nonlinear dynamics (including period-doubling and positive Lyapunov exponents) and is dissipative for c − (h + a) < 0. The original system proposed by Dadras & Momeni (2009, p. 3638) is given by equations:

\(\dot{x} = y - a x + b y z\)

\(\dot{y} = c y - x z + z\)

\(\dot{z} = d x y - h z\)

Here a introduces linear damping in the x-component, while b scales the multiplicative nonlinearity \(y z\) that folds trajectories. The parameter c controls linear growth in y (with an additional +z drive), d couples \(x y\) into the z-equation, and h sets linear damping in z. For the classical set (a=3, b=2.7, c=4.7, d=2, h=9) the system produces a two-scroll chaotic attractor; changing c alone yields a three-scroll (e.g., c=1.7) or four-scroll (e.g., c=3.9) structure, illustrating how small parameter variations reorganize the attractor’s topology.

Source: Dadras, S. & Momeni, H. R. (2009). A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors. Physics Letters A, 373(40), 3637–3642.
DOI: 10.1016/j.physleta.2009.07.088