Synthesis of piecewise-linear chaotic oscillators with prescribed eigenvalues

Circuits which realize chaotic oscillators of arbitrary degree, using a piecewise-linear element, are now well known. In such circuits, the linear portion requires, in general, resistors, inductors, and capacitors which may be positive or negative, while the piecewise-linear element has at least one negative slope. It is shown here that any oscillator based on an odd symmetrical continuous piecewise-linear element with three linear regions, and n prescribed eigenvalues in each region, can be realized by a linear circuit with positive inductance and capacitance and one linear negative resistance. It is also shown that the slopes of the piecewise-linear element may be made positive or zero. A canonic realization is given, and the technique is applied to a number of published examples.