Determining the number of scrolls in a multi-scroll chaotic oscillator under uncertainties

A trade-off analysis on the chaotic regime in a multi-scroll chaotic system and the uncertainties of its parameters is presented. The chaotic oscillator is modeled by using the state-variables approximation and its nonlinear function is represented as a piecewise linear (PWL) function. In particular, a 4-scroll chaotic system with four parameters is studied. Due to the chaotic behavior depends on the system parameters; linear and random sweeps are performed to obtain an interval for each parameter. This trust interval is used to predict the number of scrolls that can be synthesized under uncertainties and also, the implementation with an electronic circuit based on operational amplifiers. MATLAB simulations confirm the usefulness of the proposed approach.