Chau’s Circuit is a simple electronic circuit that demonstrates chaotic behavior. The circuit was developed by Leon O. Chua in 1983, and its ease of construction has made it a very popular, real-world example of chaotic systems. In order to construct a chaotic, autonomous circuit, the circuit must include three components: 1) one or more non-linear elements, 2) one or more locally active resistors, and 3) three or more energy-storage units. Chua’s Circuit is the simplest type of chaotic circuit. Its energy storage elements contain two capacitors (C1 and C2) and an inductor (L1). It also includes an active resistor (R), as well as a non-linear resistor made of two linear resistors and two diodes. Below is a sample picture of the circuit, with the far right containing a negative impedence converter.
The equations to describe Chua’s Circuit are as follows:
- Where x(t), y(t), and z(t) represent the voltage differences across C1 and C2 as well as the intensity of the current in L1, respectively. The function f(x) describes the response of the non-linear resistor, and alpha and beta are determined by the particular values of the circuit’s components. When these three equations are used to graph (x,y,z) in 3-d space, a chaotic attractor can be observed for certain values of f(x). This example is extremely similar to the Lorenz’ Attractor, in both concept and results, due to the non-linear equations the circuit is based off of. Below is an image of experimental results with Chua’s Circuit, as well as a link to an applet that models the chaotic attractor.
- Chua\’s Circuit Applet