Abstract :
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
Keywords :
chaos generators; eigenvalues and eigenfunctions; nonlinear network synthesis; oscillators; piecewise linear techniques; canonic realization; linear negative resistance; odd symmetrical continuous PWL element; piecewise-linear chaotic oscillators; piecewise-linear element; positive capacitance; positive inductance; prescribed eigenvalues; Capacitors; Chaos; Circuit synthesis; Eigenvalues and eigenfunctions; Inductance; Inductors; Linear circuits; Oscillators; Piecewise linear techniques; Resistors;
