On the trade-off between the number of scrolls and the operating frequency of the chaotic attractors

A trade-off analysis on the number of scrolls and the operating frequency is presented. To do so, nonlinear system parameters, real physical active device parameters and the operating frequency are taken into account to model the behavior of the saturated nonlinear function series approximated by a piecewise-linear description. As a consequence, not only the trade-off between the number of scrolls and the operating frequency is investigated, which depends directly on the behavior at the operating frequency of the nonlinear function, but also chaotic attractors are efficiently synthesized without the application of scaling techniques. Theoretical calculations are in good agreement with numerical simulations and a prediction on the maximum number of scrolls that can be synthesized for a particular frequency is also given.