String of scrolls from a time-delayed chaotic circuit

Abstract

Over the last few decades, complex multi-scroll chaotic attractors generated through electronic circuits have considerably been raised. Therefore, this paper concerns the design and implementation of multi-scroll chaotic attractors such as two-scrolls, three-scrolls and four-scrolls generated from a first-order delay differential equation. Modelling a time-delayed feed-back chaotic system considers a simple nonlinearity piecewise-linear (PWL) function to generate the chaotic attractors with an odd/even numbers of scrolls. The delayed feedback consists of a cascade of Bessel filters and the design of a circuit which generates a string of scrolls chaotic attractors depending on the number of intersection points of nonlinearity of PWL function with a state variable. The simulation results reveal that the multiple-scroll chaotic attractors can be successfully reproduced using PSpice. The implementation based on circuitswitching mode with simple components such as resistors, capacitors, and operational amplifiers is also presented.