TOPICS
Search

Chua's Circuit Equations


Chua's circuit equations form an autonomous dynamical system of three coupled first-order ordinary differential equations (Chua et al. 1993, Chua 2007). A dimensionless form is

x^'=alpha(y-x-f(x))
(1)
y^'=x-y+z
(2)
z^'=-betay,
(3)

where x(t), y(t), and z(t) are the state variables, primes denote derivatives with respect to dimensionless time t, and alpha and beta are positive parameters. The odd piecewise linear function f(x) describes the circuit's nonlinear response,

 f(x)=m_1x+(m_0-m_1)/2(|x+1|-|x-1|).
(4)

The slope of f(x) is m_0 for |x|<1 and m_1 for |x|>1. The system is invariant under the simultaneous sign change of x, y, and z. Its stationary states have the form (x,0,-x) with x+f(x)=0. For suitable parameters, the system exhibits a double-scroll attractor. A trajectory on it winds around two lobes in phase space (Chua 2007).


See also

Chaos, Double-Scroll Attractor, Dynamical System, Strange Attractor

Explore with Wolfram|Alpha

References

Chua, L. O.; Wu, C. W.; Huang, A.; and Zhong, G.-Q. "A Universal Circuit for Studying and Generating Chaos. I. Routes to Chaos." IEEE Trans. Circuits Syst. I 40, 732-744, 1993. https://doi.org/10.1109/81.246149.Chua, L. O. "Chua Circuit." Scholarpedia 2, 1488, 2007. https://doi.org/10.4249/scholarpedia.1488.

Cite this as:

Weisstein, Eric W. "Chua's Circuit Equations." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ChuasCircuitEquations.html

Subject classifications