Canonical realization of Chua's circuit family

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.