Synthesis of higher dimensional Chua circuits

In this paper, we present a universal method to design n-dimensional piecewise linear circuits. These circuits are described by a system of differential equation associated with a piecewise linear continuous vector-field in the n-dimensional state-space, which consists of two different linear regions. The circuits contain only two-terminal elements, one piecewise linear resistor and a number of linear resistors, capacitors and inductors. The developed method leads to a variety of structures. It is possible to design n-dimensional canonical circuits containing a minimum number of inductors as well as inductor-free circuits. A surprising result is the transformation of the 3-D Chua circuit into an inductor-free circuit that exhibits the double scroll as well. Using our approach, a theorem that specifies the restriction of eigenvalue patterns associated with a piecewise linear vector-field having at least two equilibrium points can be proved.<
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