Lü Attractor

Attractor Builder (Blender add-on)
Equations:
ẋ = a * (y - x)
ẏ = c * y - x * z
ż = x * y - b * z
Parameters:
| a = 36 | b = 3 | c = 20 |
Simulation settings:
Initial conditions: x₀ = 0.1, y₀ = 0.1, z₀ = 0.1
Method: RK4  
Time Step (dt): 0.005  
Steps: 10000  
Burn-in: 300  
Scale: 0.1

The Lü attractor was introduced in 2002 by Jian Lü and Guanrong Chen as a new three-dimensional chaotic system that bridges the gap between the classical Lorenz (1963) and Chen (1999) attractors. By continuously varying its parameters, the Lü system can exhibit a smooth transition from Lorenz-type to Chen-type chaos, revealing an intermediate form of chaotic behavior. The original system of equations (Lü & Chen, 2002, p. 660) is given as:

\[ \begin{cases} \dot{x} = a\,(y - x),\\ \dot{y} = -x z + c\,y,\\ \dot{z} = x y - b\,z, \end{cases} \]

The parameter a defines the coupling strength between variables x and y, b controls the dissipation along the z-axis, and c determines the amplification in the y direction. For a = 36, b = 3, and c in the approximate range 12.7–28.5, the system exhibits chaotic behavior, producing a double-scroll structure reminiscent of the Lorenz attractor.

Source: Lü, J., & Chen, G. (2002). A new chaotic attractor coined. International Journal of Bifurcation and Chaos, 12(3), 659–661. DOI: 10.1142/S0218127402004620