Canonical realization of Chua's circuit family
- 1 July 1990
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuits and Systems
- Vol. 37 (7), 885-902
- https://doi.org/10.1109/31.55064
Abstract
A new canonical piecewise-linear circuit capable of realizing every member of the Chua's circuit family is presented. It contains only six two-terminal elements: five of them are linear resistors, capacitors, and inductors, and only one element is a three-segment piecewise-linear resistor. It is canonical in the sense that (1) it can exhibit all possible phenomena associated with any three-region symmetric piecewise-linear continuous vector fields and (2) it contains the minimum number of circuit elements needed for such a circuit. This circuit is used to prove a theorem that specifies the constraint on the types of eigenvalue patterns associated with a piecewise-linear continuous vector field having three equilibrium points. This theorem has an explicit physical meaning and unifies the corresponding theorem in the work of L.O. Chua et al. (1986) and C.P. Silva and L.O. Chua et al. (1988). Also presented are some computer simulation results for this circuit, including some new attractors that have not been observed before.Keywords
This publication has 9 references indexed in Scilit:
- The overdamped double‐scroll family. Part I: Piecewise‐linear geometry and normal formInternational Journal of Circuit Theory and Applications, 1988
- Chaos via torus breakdownIEEE Transactions on Circuits and Systems, 1987
- Transfer maps and return maps for piecewise-linear three-region dynamical systemsInternational Journal of Circuit Theory and Applications, 1987
- Chua's circuit familyProceedings of the IEEE, 1987
- The double scroll familyIEEE Transactions on Circuits and Systems, 1986
- The double scroll bifurcationsInternational Journal of Circuit Theory and Applications, 1986
- The double scrollIEEE Transactions on Circuits and Systems, 1985
- Chaos in piecewise-linear systemsPhysical Review A, 1983
- Chaos in a three-dimensional single loop feedback system with a piecewice linear feedbackk functionJournal of Mathematical Analysis and Applications, 1981