Chen Attractor

Attractor Builder (Blender add-on)
Equations:
ẋ = a * (y - x)
ẏ = (c - a) * x - x * z + c * y
ż = x * y - b * z
Parameters:
| a = 35 | b = 3 | c = 28 |
Simulation settings:
Initial state: x₀ = 0, y₀ = 1, z₀ = 1
Method: RK4
Time Step (dt): 0.005
Steps: 20000
Burn-in: 1000
Scale: 0.1

The Chen attractor was introduced in 1999 by Guanrong Chen and Tetsushi Ueta as a new chaotic system discovered during research on anticontrol of chaos — the process of deliberately inducing chaos in an otherwise nonchaotic system. Although its equations closely resemble those of the Lorenz system, the Chen system is not topologically equivalent to either the Lorenz or the Rössler attractors. Its discovery provided an important example showing that small structural differences in nonlinear dynamical equations can produce distinct types of chaotic behavior. The original system proposed by Chen & Ueta (1999, p. 1465) is given by equations:

\(\dot{x} = a (y - x)\)

\(\dot{y} = (c - a)x - xz + cy\)

\(\dot{z} = xy - bz\)

In this model, the parameter a represents the strength of the coupling between the x and y components, b governs the rate of dissipation along the z axis, and c influences both the linear amplification and the nonlinear feedback through the y- and xz-terms. For the classical parameter set (a=35, b=3, c=28), the system exhibits a complex double-scroll chaotic attractor resembling the Lorenz structure but with different equilibrium topology. Despite visual similarity, no linear or nonlinear coordinate transformation can convert the Chen system into the Lorenz system — proving their dynamical inequivalence.

Źródło:
Chen, G. & Ueta, T. (1999). Yet Another Chaotic Attractor. International Journal of Bifurcation and Chaos, 9 (7), 1465–1466. DOI: 10.1142/S0218127499001024