# 2009 Research Summary

## Qualitative Dynamics of Chua's Circuit

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Bharathwaj Muthuswamy and Leon O. Chua

In this project we investigate exotic implementations of Chua's circuit, the paradigm for generating chaotic attractors. Specifically, we are working on rigorously proving chaos in the 4-Element Chua's circuit and memristor-based chaotic circuits.

Figure 1: A schematic of Chua's circuit. There are a variety of methods to implement the nonlinear element (Chua diode).

- [1]
- L. O. Chua, "The Genesis of Chua's Circuit,"
*Archiv fur Elektronik und Uebertragungstechnik,*Vol. 46, No. 4, 1992, pp. 250-257. - [2]
- M. P. Kennedy, "Robust Op-Amp Realization of Chua's Circuit,"
*Frequenz,*Vol. 46, No. 3-4, March-April 1992, pp. 66-80. - [3]
- R. Kilic, "A Comparative Study on Realization of Chua's Circuit: Hybrid Realizations of Chua's Circuit Combining the Circuit Topologies Proposed for Chua's Diode and Inductor Elements,"
*IJBC,*Vol. 13, No. 6, 2003, pp. 1475-1493. - [4]
- T. Matsumoto, "A Chaotic Attractor from Chua's Circuit,"
*IEEE Trans. Circuits and Systems,*Vol. 31, No. 12, 1984, pp. 1055-1058. - [5]
- L. P. Shil'nikov, "Chua's Circuit: Rigorous Results and Future Problems,"
*IEEE Trans. Circuits and Systems I-Fundamental Theory and Applications,*Vol. 40, No. 10, 1993, pp. 784-786. - [6]
- L. O. Chua, "Memristor--The Missing Circuit Element,"
*IEEE Transactions on Circuit Theory,*Vol. 18, No. 5, pp. 507-519.