Chua Attractor

Attractor Builder (Blender Add-on)
Equations:
ẋ = k*p*(y - x - (b*x + 0.5*(a - b)*(fabs(x + 1) - fabs(x - 1))))
ẏ = k*(x - y + z)
ż = k*(-q*y - r*z)
Parameters:
| a = 0.1 | b = -0.48 | k = 1 | p = -1.3 | q = -0.0136 | r = -0.0297 |
Simulation Settings:
Initial state: x₀ = 0.1, y₀ = 0.0, z₀ = 0.0  
Method: DP5  
Tolerance: 0.0001  
Min step: 0.0001  
Max step: 0.1  
Steps: 20000  
Burn-in: 500  
Scale: 0.7

The Chua attractor is one of the classic examples of chaos arising in physical electronic systems. In his work on nonlinear dynamic networks, Leon O. Chua (1983) sought simple feedback circuits capable of producing complex, nonperiodic trajectories using only a single nonlinear element. Building on this idea, Takashi Matsumoto (1984) presented the first experimental and numerical demonstration of chaotic behavior in a real RLC circuit containing the now-famous Chua diode. The final dimensionless form of the oscillator proposed by Chua was introduced in 1995 and is given by the system:

\( \dfrac{dx}{dt} = k \alpha (\,y - x - f(x)\,), \)

\( \dfrac{dy}{dt} = k (\,x - y + z\,), \)

\( \dfrac{dz}{dt} = k (\, -\beta y - \gamma z\,). \)

In this formulation, the nonlinearity is introduced through the piecewise-linear function \( f(x) = b x + \tfrac{1}{2}(a - b)(|x + 1| - |x - 1|) \), which represents the characteristic of the so-called Chua diode.

Sources:

Matsumoto, T. (1984). A chaotic attractor from Chua’s circuit. IEEE Transactions on Circuits and Systems, 31(12), 1055–1058. https://doi.org/10.1109/TCS.1984.1085459

Chua, L. O. (1983). Dynamic Nonlinear Networks: State-of-the-Art. IEEE International Symposium on Circuits and Systems, 12, 2–6. https://doi.org/10.1109/TCS.1980.1084745

Chua, L. O. (1995). A glimpse of nonlinear phenomena from Chua’s oscillator. Philosophical Transactions of the Royal Society A, 353(1701), 3–12. https://www.jstor.org/stable/54515