Christophe LETELLIER
09/06/2012

**Leon Chua**

The Chua circuit is an *RLC* circuit with four linear elements (two
capacitors, one resistor and one inductor) and a nonlinear diode, and
can be modeled by a system of three differential equations. The
equations for the Chua circuit are [1] :

where

With parameter values as *G*=0.7, *C*_{1}=1/9, *C*_{2}=1, *m*_{0}=-0.5, *m*_{1}=-0.8, *B*_{p}=1 and *L*=1/7, *m*_{1}=-5/7 and , a chaotic attractor is obtained (Fig. 1).

**Fig. 1 : Chaotic attractor solution to the Chua circuit.**

In a beautiful paper [2], the topology of this attractor was described in terms of a branch manifold (template) as shown in Fig. 2. The first electronic circuit with a five-segment odd-symmetric *v*-*i* characteristic by Farhad Ayrom (Berkeley University) and Guo-Qun Zhong (Academia Sinica, Guangzhou, People’s Republic of China), designed an electronic circuit [3]. A historical account on the discovery of this circuit is given in [4]. According to Robert Ghrist and Philip Holmes, this attractor is characterized by a template which contains all possible knots [5].

**Fig. 2 : Template for the double-scroll attractor.**

[1] **T. Matsumoto**, A chaotic attractor from Chua’s circuit, *IEEE Transactions on Circuits & Systems*, **31** (12), 1055-1058, 1984.

[2] **T. Matsumoto, L. O. Chua & M. Komuro**, The double scroll, *IEEE Transactions on Circuits & Systems*, **32** (8), 798-818, 1985.

[3] **G.-Q. Zhong & F. Ayrom**, Experimental confirmation of chaos from Chua’s circuit, *Circuit Theory and Applications*, **13** (1), 93-98, 1985.

[4] **C. Letellier & J.-M. Ginoux**, Development of the nonlinear dynamical systems theory from radio-engineering to electronics, *International Journal of Bifurcation & Chaos*, **19** (7), 2131–2163, 2009.

[5] **R. Ghrist & P. Holmes**, An ODE whose solutions contain all knots and links, *International Journal of Bifurcation &
Chaos*, **6** (5), 779-800, 1996.